Solutions for homogeneous equations

# Include <cstdio>

 

Long long Mod (long a, long B)

{Return (a % B + B) % B ;}

 

Struct triple {long d, X, Y ;};

 

Long long Euclid (Long a, long B)

{

If (B = 0) return;

Else return Euclid (B, MOD (a, B ));

}

 

Triple extended_euclid (long a, long B)

{

Triple result;

If (B = 0)

{Result. d = A; Result. x = 1; Result. Y = 0 ;}

Else

{

Triple EE = extended_euclid (B, MOD (a, B ));

Result. d = ee. D;

Result. x = ee. Y;

Result. Y = ee. X-(A/B) * ee. Y;

}

Return result;

}

 

Long long mles (long a, long B, long N)

{

Triple EE = extended_euclid (A, N );

If (mod (B, ee. d) Return-1;

Else return Mod (EE. x * (B/EE. D), N/EE. D );

}

 

Int main ()

{

Long long x, y, m, n, l;

While (scanf ("% i64d % i64d % i64d % i64d % i64d", & X, & Y, & M, & N, & L )! = EOF)

{

Long long mles;

Mles = mles (m-N, Y-X, L );

/* Enter the following three parameters: A, B, and N to obtain the limit solution (ax-B) % n = 0.

If-1 is returned, this equation has no solution. */

If (mles <0)

Printf ("impossible \ n ");

Else

Printf ("% i64d \ n", mles );

}

Return 0;

}