ZOJ 3609 Modular Inverse(扩展欧几里得求逆元）

The modular modular multiplicative inverse of an integer a modulo m is an integer x such that 

a-1≡x (mod m)

. This is equivalent to 

ax≡1 (mod m)

.

Input

There are multiple test cases. The first line of input is an integer T ≈ 2000 indicating the number of test cases.Each test case contains two integers 0 < a ≤ 1000 and 0 < m ≤ 1000.

Output

For each test case, output the smallest positive x. If such x doesn't exist, output "Not Exist".

Sample Input

3
3 11
4 12
5 13

Sample Output

4
Not Exist

8#include<cstdio>
#include<cmath>
using namespace std;
typedef long long ll;
ll exten_gcd(ll a,ll b,ll& x,ll& y)
{
ll d=a;
if(b)
{
d=exten_gcd(b,a%b,y,x);
y-=a/b*x;
}
else x=1,y=0;
return d;
}
int main()
{
int T;scanf("%d",&T);
while(T--)
{
ll a,m;
scanf("%lld%lld",&a,&m);
ll x,y,s;
s=exten_gcd(a,m,x,y);
if(s!=1)printf("Not Exist\n");
else
{
x%=m;
if(x<=0)x+=m;
printf("%lld\n",x);//x可能等于m，开始写成(x%m+m)%m wa了
}
}
return 0;
}