//
// Cforall Version 1.0.0 Copyright (C) 2016 University of Waterloo
//
// The contents of this file are covered under the licence agreement in the
// file "LICENCE" distributed with Cforall.
//
// gmp --
//
// Author           : Peter A. Buhr
// Created On       : Tue Apr 19 08:43:43 2016
// Last Modified By : Peter A. Buhr
// Last Modified On : Mon Sep  4 09:54:33 2017
// Update Count     : 20
//

// https://gmplib.org/gmp-man-6.1.1.pdf

#pragma once

#include <gmp.h>										// GNU multi-precise integers
#include <fstream>										// sout

struct Int { mpz_t mpz; };								// wrap GMP implementation

// constructor
static inline void ?{}( Int & this ) { mpz_init( this.mpz ); }
static inline void ?{}( Int & this, Int init ) { mpz_init_set( this.mpz, init.mpz ); }
static inline void ?{}( Int & this, zero_t ) { mpz_init_set_si( this.mpz, 0 ); }
static inline void ?{}( Int & this, one_t ) { mpz_init_set_si( this.mpz, 1 ); }
static inline void ?{}( Int & this, signed long int init ) { mpz_init_set_si( this.mpz, init ); }
static inline void ?{}( Int & this, unsigned long int init ) { mpz_init_set_ui( this.mpz, init ); }
static inline void ?{}( Int & this, const char * val ) { if ( mpz_init_set_str( this.mpz, val, 0 ) ) abort(); }
static inline void ^?{}( Int & this ) { mpz_clear( this.mpz ); }

// literal
static inline Int ?`mp( signed long int init ) { return (Int){ init }; }
static inline Int ?`mp( unsigned long int init ) { return (Int){ init }; }
static inline Int ?`mp( const char * init ) { return (Int){ init }; }

// assignment
static inline Int ?=?( Int & lhs, Int rhs ) { mpz_set( lhs.mpz, rhs.mpz ); return lhs; }
static inline Int ?=?( Int & lhs, long int rhs ) { mpz_set_si( lhs.mpz, rhs ); return lhs; }
static inline Int ?=?( Int & lhs, unsigned long int rhs ) { mpz_set_ui( lhs.mpz, rhs ); return lhs; }
static inline Int ?=?( Int & lhs, const char * rhs ) { if ( mpz_set_str( lhs.mpz, rhs, 0 ) ) { printf( "invalid string conversion\n" ); abort(); } return lhs; }

static inline char ?=?( char & lhs, Int rhs ) { char val = mpz_get_si( rhs.mpz ); lhs = val; return lhs; }
static inline short int ?=?( short int & lhs, Int rhs ) { short int val = mpz_get_si( rhs.mpz ); lhs = val; return lhs; }
static inline int ?=?( int & lhs, Int rhs ) { int val = mpz_get_si( rhs.mpz ); lhs = val; return lhs; }
static inline long int ?=?( long int & lhs, Int rhs ) { long int val = mpz_get_si( rhs.mpz ); lhs = val; return lhs; }
static inline unsigned char ?=?( unsigned char & lhs, Int rhs ) { unsigned char val = mpz_get_ui( rhs.mpz ); lhs = val; return lhs; }
static inline unsigned short int ?=?( unsigned short int & lhs, Int rhs ) { unsigned short int val = mpz_get_ui( rhs.mpz ); lhs = val; return lhs; }
static inline unsigned int ?=?( unsigned int & lhs, Int rhs ) { unsigned int val = mpz_get_ui( rhs.mpz ); lhs = val; return lhs; }
static inline unsigned long int ?=?( unsigned long int & lhs, Int rhs ) { unsigned long int val = mpz_get_ui( rhs.mpz ); lhs = val; return lhs; }

// conversions
static inline long int narrow( Int val ) { return mpz_get_si( val.mpz ); }
static inline unsigned long int narrow( Int val ) { return mpz_get_ui( val.mpz ); }

// comparison
static inline int ?==?( Int oper1, Int oper2 ) { return mpz_cmp( oper1.mpz, oper2.mpz ) == 0; }
static inline int ?==?( Int oper1, long int oper2 ) { return mpz_cmp_si( oper1.mpz, oper2 ) == 0; }
static inline int ?==?( long int oper2, Int oper1 ) { return mpz_cmp_si( oper1.mpz, oper2 ) == 0; }
static inline int ?==?( Int oper1, unsigned long int oper2 ) { return mpz_cmp_ui( oper1.mpz, oper2 ) == 0; }
static inline int ?==?( unsigned long int oper2, Int oper1 ) { return mpz_cmp_ui( oper1.mpz, oper2 ) == 0; }

static inline int ?!=?( Int oper1, Int oper2 ) { return ! ( oper1 == oper2 ); }
static inline int ?!=?( Int oper1, long int oper2 ) { return ! ( oper1 == oper2 ); }
static inline int ?!=?( long int oper1, Int oper2 ) { return ! ( oper1 == oper2 ); }
static inline int ?!=?( Int oper1, unsigned long int oper2 ) { return ! ( oper1 == oper2 ); }
static inline int ?!=?( unsigned long int oper1, Int oper2 ) { return ! ( oper1 == oper2 ); }

static inline int ?<?( Int oper1, Int oper2 ) { return mpz_cmp( oper1.mpz, oper2.mpz ) < 0; }
static inline int ?<?( Int oper1, long int oper2 ) { return mpz_cmp_si( oper1.mpz, oper2 ) < 0; }
static inline int ?<?( long int oper2, Int oper1 ) { return mpz_cmp_si( oper1.mpz, oper2 ) < 0; }
static inline int ?<?( Int oper1, unsigned long int oper2 ) { return mpz_cmp_ui( oper1.mpz, oper2 ) < 0; }
static inline int ?<?( unsigned long int oper2, Int oper1 ) { return mpz_cmp_ui( oper1.mpz, oper2 ) < 0; }

static inline int ?<=?( Int oper1, Int oper2 ) { return mpz_cmp( oper1.mpz, oper2.mpz ) <= 0; }
static inline int ?<=?( Int oper1, long int oper2 ) { return mpz_cmp_si( oper1.mpz, oper2 ) <= 0; }
static inline int ?<=?( long int oper2, Int oper1 ) { return mpz_cmp_si( oper1.mpz, oper2 ) <= 0; }
static inline int ?<=?( Int oper1, unsigned long int oper2 ) { return mpz_cmp_ui( oper1.mpz, oper2 ) <= 0; }
static inline int ?<=?( unsigned long int oper2, Int oper1 ) { return mpz_cmp_ui( oper1.mpz, oper2 ) <= 0; }

static inline int ?>?( Int oper1, Int oper2 ) { return ! ( oper1 <= oper2 ); }
static inline int ?>?( Int oper1, long int oper2 ) { return ! ( oper1 <= oper2 ); }
static inline int ?>?( long int oper1, Int oper2 ) { return ! ( oper1 <= oper2 ); }
static inline int ?>?( Int oper1, unsigned long int oper2 ) { return ! ( oper1 <= oper2 ); }
static inline int ?>?( unsigned long int oper1, Int oper2 ) { return ! ( oper1 <= oper2 ); }

static inline int ?>=?( Int oper1, Int oper2 ) { return ! ( oper1 < oper2 ); }
static inline int ?>=?( Int oper1, long int oper2 ) { return ! ( oper1 < oper2 ); }
static inline int ?>=?( long int oper1, Int oper2 ) { return ! ( oper1 < oper2 ); }
static inline int ?>=?( Int oper1, unsigned long int oper2 ) { return ! ( oper1 < oper2 ); }
static inline int ?>=?( unsigned long int oper1, Int oper2 ) { return ! ( oper1 < oper2 ); }

// arithmetic
static inline Int +?( Int oper ) { Int pos; mpz_set( pos.mpz, oper.mpz ); return pos; }
static inline Int -?( Int oper ) { Int neg; mpz_neg( neg.mpz, oper.mpz ); return neg; }
static inline Int ~?( Int oper ) { Int comp; mpz_com( comp.mpz, oper.mpz ); return comp; }

static inline Int ?&?( Int oper1, Int oper2 ) { Int conjunction; mpz_and( conjunction.mpz, oper1.mpz, oper2.mpz ); return conjunction; }
static inline Int ?&?( Int oper1, long int oper2 ) { Int conjunction, temp; mpz_set_si( temp.mpz, oper2 ); mpz_and( conjunction.mpz, oper1.mpz, temp.mpz ); return conjunction; }
static inline Int ?&?( long int oper1, Int oper2 ) { Int conjunction, temp; mpz_set_si( temp.mpz, oper1 ); mpz_and( conjunction.mpz, temp.mpz, oper2.mpz ); return conjunction; }
static inline Int ?&?( Int oper1, unsigned long int oper2 ) { Int conjunction, temp; mpz_set_ui( temp.mpz, oper2 ); mpz_and( conjunction.mpz, oper1.mpz, temp.mpz ); return conjunction; }
static inline Int ?&?( unsigned long int oper1, Int oper2 ) { Int conjunction, temp; mpz_set_ui( temp.mpz, oper1 ); mpz_and( conjunction.mpz, temp.mpz, oper2.mpz ); return conjunction; }
static inline Int ?&=?( Int & lhs, Int rhs ) { return lhs = lhs & rhs; }

static inline Int ?|?( Int oper1, Int oper2 ) { Int disjunction; mpz_ior( disjunction.mpz, oper1.mpz, oper2.mpz ); return disjunction; }
static inline Int ?|?( Int oper1, long int oper2 ) { Int disjunction, temp; mpz_set_si( temp.mpz, oper2 ); mpz_ior( disjunction.mpz, oper1.mpz, temp.mpz ); return disjunction; }
static inline Int ?|?( long int oper1, Int oper2 ) { Int disjunction, temp; mpz_set_si( temp.mpz, oper1 ); mpz_ior( disjunction.mpz, temp.mpz, oper2.mpz ); return disjunction; }
static inline Int ?|?( Int oper1, unsigned long int oper2 ) { Int disjunction, temp; mpz_set_ui( temp.mpz, oper2 ); mpz_ior( disjunction.mpz, oper1.mpz, temp.mpz ); return disjunction; }
static inline Int ?|?( unsigned long int oper1, Int oper2 ) { Int disjunction, temp; mpz_set_ui( temp.mpz, oper1 ); mpz_ior( disjunction.mpz, temp.mpz, oper2.mpz ); return disjunction; }
static inline Int ?|=?( Int & lhs, Int rhs ) { return lhs = lhs | rhs; }

static inline Int ?^?( Int oper1, Int oper2 ) { Int disjunction; mpz_xor( disjunction.mpz, oper1.mpz, oper2.mpz ); return disjunction; }
static inline Int ?^?( Int oper1, long int oper2 ) { Int disjunction, temp; mpz_set_si( temp.mpz, oper2 ); mpz_ior( disjunction.mpz, oper1.mpz, temp.mpz ); return disjunction; }
static inline Int ?^?( long int oper1, Int oper2 ) { Int disjunction, temp; mpz_set_si( temp.mpz, oper1 ); mpz_ior( disjunction.mpz, temp.mpz, oper2.mpz ); return disjunction; }
static inline Int ?^?( Int oper1, unsigned long int oper2 ) { Int disjunction, temp; mpz_set_ui( temp.mpz, oper2 ); mpz_ior( disjunction.mpz, oper1.mpz, temp.mpz ); return disjunction; }
static inline Int ?^?( unsigned long int oper1, Int oper2 ) { Int disjunction, temp; mpz_set_ui( temp.mpz, oper1 ); mpz_ior( disjunction.mpz, temp.mpz, oper2.mpz ); return disjunction; }
static inline Int ?^=?( Int & lhs, Int rhs ) { return lhs = lhs ^ rhs; }

static inline Int ?+?( Int addend1, Int addend2 ) { Int sum; mpz_add( sum.mpz, addend1.mpz, addend2.mpz ); return sum; }
static inline Int ?+?( Int addend1, long int addend2 ) { Int sum; if ( addend2 >= 0 ) mpz_add_ui( sum.mpz, addend1.mpz, addend2 ); else mpz_sub_ui( sum.mpz, addend1.mpz, -addend2 ); return sum; }
static inline Int ?+?( long int addend2, Int addend1 ) { Int sum; if ( addend2 >= 0 ) mpz_add_ui( sum.mpz, addend1.mpz, addend2 ); else mpz_sub_ui( sum.mpz, addend1.mpz, -addend2 ); return sum; }
static inline Int ?+?( Int addend1, unsigned long int addend2 ) { Int sum; mpz_add_ui( sum.mpz, addend1.mpz, addend2 ); return sum; }
static inline Int ?+?( unsigned long int addend2, Int addend1 ) { Int sum; mpz_add_ui( sum.mpz, addend1.mpz, addend2 ); return sum; }
static inline Int ?+=?( Int & lhs, Int rhs ) { return lhs = lhs + rhs; }
static inline Int ?+=?( Int & lhs, long int rhs ) { return lhs = lhs + rhs; }
static inline Int ?+=?( Int & lhs, unsigned long int rhs ) { return lhs = lhs + rhs; }
static inline Int ++?( Int & lhs ) { return lhs += 1; }
static inline Int ?++( Int & lhs ) { Int ret = lhs; lhs += 1; return ret; }

static inline Int ?-?( Int minuend, Int subtrahend ) { Int diff; mpz_sub( diff.mpz, minuend.mpz, subtrahend.mpz ); return diff; }
static inline Int ?-?( Int minuend, long int subtrahend ) { Int diff; if ( subtrahend >= 0 ) mpz_sub_ui( diff.mpz, minuend.mpz, subtrahend ); else mpz_add_ui( diff.mpz, minuend.mpz, -subtrahend ); return diff; }
static inline Int ?-?( long int minuend, Int subtrahend ) { Int diff; if ( subtrahend >= 0 ) mpz_ui_sub( diff.mpz, minuend, subtrahend.mpz ); else { mpz_add_ui( diff.mpz, subtrahend.mpz, -minuend ); mpz_neg( diff.mpz, diff.mpz ); } return diff; }
static inline Int ?-?( Int minuend, unsigned long int subtrahend ) { Int diff; mpz_sub_ui( diff.mpz, minuend.mpz, subtrahend ); return diff; }
static inline Int ?-?( unsigned long int minuend, Int subtrahend ) { Int diff; mpz_ui_sub( diff.mpz, minuend, subtrahend.mpz ); return diff; }
static inline Int ?-=?( Int & lhs, Int rhs ) { return lhs = lhs - rhs; }
static inline Int ?-=?( Int & lhs, long int rhs ) { return lhs = lhs - rhs; }
static inline Int ?-=?( Int & lhs, unsigned long int rhs ) { return lhs = lhs - rhs; }
static inline Int --?( Int & lhs ) { return lhs -= 1; }
static inline Int ?--( Int & lhs ) { Int ret = lhs; lhs -= 1; return ret; }

static inline Int ?*?( Int multiplicator, Int multiplicand ) { Int product; mpz_mul( product.mpz, multiplicator.mpz, multiplicand.mpz ); return product; }
static inline Int ?*?( Int multiplicator, long int multiplicand ) { Int product; mpz_mul_si( product.mpz, multiplicator.mpz, multiplicand ); return product; }
static inline Int ?*?( long int multiplicand, Int multiplicator ) { Int product; mpz_mul_si( product.mpz, multiplicator.mpz, multiplicand ); return product; }
static inline Int ?*?( Int multiplicator, unsigned long int multiplicand ) { Int product; mpz_mul_ui( product.mpz, multiplicator.mpz, multiplicand ); return product; }
static inline Int ?*?( unsigned long int multiplicand, Int multiplicator ) { Int product; mpz_mul_ui( product.mpz, multiplicator.mpz, multiplicand ); return product; }
static inline Int ?*=?( Int & lhs, Int rhs ) { return lhs = lhs * rhs; }
static inline Int ?*=?( Int & lhs, long int rhs ) { return lhs = lhs * rhs; }
static inline Int ?*=?( Int & lhs, unsigned long int rhs ) { return lhs = lhs * rhs; }

// some code for operators "/" and "%" taken from g++ gmpxx.h
static inline Int ?/?( Int dividend, Int divisor ) { Int quotient; mpz_tdiv_q( quotient.mpz, dividend.mpz, divisor.mpz ); return quotient; }
static inline Int ?/?( Int dividend, unsigned long int divisor ) { Int quotient; mpz_tdiv_q_ui( quotient.mpz, dividend.mpz, divisor ); return quotient; }
static inline Int ?/?( unsigned long int dividend, Int divisor ) {
	Int quotient;
    if ( mpz_sgn( divisor.mpz ) >= 0 ) {
		if ( mpz_fits_ulong_p( divisor.mpz ) )
			mpz_set_ui( quotient.mpz, dividend / mpz_get_ui( divisor.mpz ) );
		else
			mpz_set_ui( quotient.mpz, 0 );
	} else {
		mpz_neg( quotient.mpz, divisor.mpz );
		if ( mpz_fits_ulong_p( quotient.mpz ) ) {
			mpz_set_ui( quotient.mpz, dividend / mpz_get_ui( quotient.mpz ) );
			mpz_neg( quotient.mpz, quotient.mpz );
		} else
			mpz_set_ui( quotient.mpz, 0 );
	} // if
	return quotient;
} // ?/?
static inline Int ?/?( Int dividend, long int divisor ) {
	Int quotient;
    if ( divisor >= 0 )
		mpz_tdiv_q_ui( quotient.mpz, dividend.mpz, divisor );
    else {
		mpz_tdiv_q_ui( quotient.mpz, dividend.mpz, -divisor );
		mpz_neg( quotient.mpz, quotient.mpz );
	} // if
	return quotient;
} // ?/?
static inline Int ?/?( long int dividend, Int divisor ) {
	Int quotient;
    if ( mpz_fits_slong_p( divisor.mpz ) )
		mpz_set_si( quotient.mpz, dividend / mpz_get_si( divisor.mpz ) );
    else {
        // if divisor is bigger than a long then the quotient must be zero, unless dividend==LONG_MIN and
        // dividend==-LONG_MIN in which case the quotient is -1
        mpz_set_si( quotient.mpz, mpz_cmpabs_ui( divisor.mpz, (dividend >= 0 ? dividend : -dividend)) == 0 ? -1 : 0 );
	} // if
	return quotient;
} // ?/?
static inline Int ?/=?( Int & lhs, Int rhs ) { return lhs = lhs / rhs; }
static inline Int ?/=?( Int & lhs, long int rhs ) { return lhs = lhs / rhs; }
static inline Int ?/=?( Int & lhs, unsigned long int rhs ) { return lhs = lhs / rhs; }

static inline [ Int, Int ] div( Int dividend, Int divisor ) { Int quotient, remainder; mpz_fdiv_qr( quotient.mpz, remainder.mpz, dividend.mpz, divisor.mpz ); return [ quotient, remainder ]; }
static inline [ Int, Int ] div( Int dividend, unsigned long int divisor ) { Int quotient, remainder; mpz_fdiv_qr_ui( quotient.mpz, remainder.mpz, dividend.mpz, divisor ); return [ quotient, remainder ]; }

static inline Int ?%?( Int dividend, Int divisor ) { Int remainder; mpz_tdiv_r( remainder.mpz, dividend.mpz, divisor.mpz ); return remainder; }
static inline Int ?%?( Int dividend, unsigned long int divisor ) { Int remainder; mpz_tdiv_r_ui( remainder.mpz, dividend.mpz, divisor ); return remainder; }
static inline Int ?%?( unsigned long int dividend, Int divisor ) {
	Int remainder;
    if ( mpz_sgn( divisor.mpz ) >= 0 ) {
		if ( mpz_fits_ulong_p( divisor.mpz ) )
			mpz_set_ui( remainder.mpz, dividend % mpz_get_ui( divisor.mpz ) );
		else
			mpz_set_ui( remainder.mpz, dividend );
	} else {
		mpz_neg( remainder.mpz, divisor.mpz );
		if ( mpz_fits_ulong_p( remainder.mpz ) )
			mpz_set_ui( remainder.mpz, dividend % mpz_get_ui( remainder.mpz ) );
		else
			mpz_set_ui( remainder.mpz, dividend );
	} // if
	return remainder;
} // ?%?
static inline Int ?%?( Int dividend, long int divisor ) {
	Int remainder;
    mpz_tdiv_r_ui( remainder.mpz, dividend.mpz, (divisor >= 0 ? divisor : -divisor));
	return remainder;
} // ?%?
static inline Int ?%?( long int dividend, Int divisor ) {
	Int remainder;
    if ( mpz_fits_slong_p( divisor.mpz ) )
		mpz_set_si( remainder.mpz, dividend % mpz_get_si( divisor.mpz ) );
	else {
		// if divisor is bigger than a long then the remainder is dividend unchanged, unless dividend==LONG_MIN and
		// dividend==-LONG_MIN in which case the remainder is 0
        mpz_set_si( remainder.mpz, mpz_cmpabs_ui( divisor.mpz, (dividend >= 0 ? dividend : -dividend)) == 0 ? 0 : dividend);
	} // if
	return remainder;
} // ?%?
static inline Int ?%=?( Int & lhs, Int rhs ) { return lhs = lhs % rhs; }
static inline Int ?%=?( Int & lhs, long int rhs ) { return lhs = lhs % rhs; }
static inline Int ?%=?( Int & lhs, unsigned long int rhs ) { return lhs = lhs % rhs; }

static inline Int ?<<?( Int shiften, mp_bitcnt_t shift ) { Int shifted; mpz_mul_2exp( shifted.mpz, shiften.mpz, shift ); return shifted; }
static inline Int ?<<=?( Int & lhs, mp_bitcnt_t shift ) { return lhs = lhs << shift; }
static inline Int ?>>?( Int shiften, mp_bitcnt_t shift ) { Int shifted; mpz_fdiv_q_2exp( shifted.mpz, shiften.mpz, shift ); return shifted; }
static inline Int ?>>=?( Int & lhs, mp_bitcnt_t shift ) { return lhs = lhs >> shift; }

// number functions
static inline Int abs( Int oper ) { Int positive; mpz_abs( positive.mpz, oper.mpz ); return positive; }
static inline Int fact( unsigned long int N ) { Int factorial; mpz_fac_ui( factorial.mpz, N ); return factorial; }
static inline Int gcd( Int oper1, Int oper2 ) { Int gcdret; mpz_gcd( gcdret.mpz, oper1.mpz, oper2.mpz ); return gcdret; }
static inline Int pow( Int base, unsigned long int exponent ) { Int power; mpz_pow_ui( power.mpz, base.mpz, exponent ); return power; }
static inline Int pow( unsigned long int base, unsigned long int exponent ) { Int power; mpz_ui_pow_ui( power.mpz, base, exponent ); return power; }
static inline void srandom( gmp_randstate_t state ) { gmp_randinit_default( state ); }
static inline Int random( gmp_randstate_t state, mp_bitcnt_t n ) { Int rand; mpz_urandomb( rand.mpz, state, n ); return rand; }
static inline Int random( gmp_randstate_t state, Int n ) { Int rand; mpz_urandomm( rand.mpz, state, n.mpz ); return rand; }
static inline Int random( gmp_randstate_t state, mp_size_t max_size ) { Int rand; mpz_random( rand.mpz, max_size ); return rand; }
static inline int sgn( Int oper ) { return mpz_sgn( oper.mpz ); }
static inline Int sqrt( Int oper ) { Int root; mpz_sqrt( root.mpz, oper.mpz ); return root; }

// I/O
static inline forall( dtype istype | istream( istype ) )
istype * ?|?( istype * is, Int & mp ) {
 	gmp_scanf( "%Zd", &mp );
 	return is;
} // ?|?

static inline forall( dtype ostype | ostream( ostype ) )
ostype * ?|?( ostype * os, Int mp ) {
	if ( sepPrt( os ) ) fmt( os, "%s", sepGetCur( os ) );
	gmp_printf( "%Zd", mp.mpz );
	sepOn( os );
 	return os;
} // ?|?

// Local Variables: //
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// tab-width: 4 //
// End: //