2012 Congruence equation

Congruence equation Title Description

The minimum positive integer solution for ax≡1 (mod b) of the x congruence equation is obtained.

Enter a description

Enter only one row, containing two positive integers a, b, separated by a space.

Output Description

The output has only one row containing a positive integer x0, or a minimum positive integer solution, and the input data guarantees there must be a solution.

Sample Input

3 10

Sample Output

7

data range and tips

For 40% of data, 2≤b≤1,000;
For 60% of data, 2≤b≤50,000,000
For 100% of data, 2≤a, b≤2,000,000,000

//the topic is a*x=1+b*y;//can be converted into A*x+b*y=1;//naked expansion of Euclid;//the time will be added to the positive;//B*x+a%b*y=1 = b*x+ (a-b* (A/b)) *y=1 =>a*y+b* (x (A/b) *y) =1;#include <cstdio>intA,b,x,y,ans;intEXGCD (intAintBint&x,int&y) {    if(b==0) {a=1; x=1; y=0;return 1;} intG=EXGCD (b,a%b,x,y), Z; Z=x;x=y;y=z-(A/b) *y; returnG;}intMain () {scanf ("%d%d",&a,&b); Ans=EXGCD (a,b,x,y);  while(x<0) x+=b; printf ("%d", x); return 0;}

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2012 Congruence equation