lightoj 1078 - Integer Divisibility 【同余定理】

1078 - Integer Divisibility

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Time Limit: 2 second(s)

Memory Limit: 32 MB

If an integer is not divisible by 2 or 5, some multiple of that number in decimal notation is a sequence of only a digit. Now you are given the number and the only allowable digit, you should report the number of digits of such multiple.

For example you have to find a multiple of 3 which contains only 1's. Then the result is 3 because is 111 (3-digit) divisible by 3. Similarly if you are finding some multiple of 7 which contains only 3's then, the result is 6, because 333333 is divisible
by 7.

Input

Input starts with an integer T (≤ 300), denoting the number of test cases.

Each case will contain two integers n (0 < n ≤ 106 and n will not be divisible by 2 or 5) and the allowable digit (1 ≤ digit ≤ 9).

Output

For each case, print the case number and the number of digits of such multiple. If several solutions are there; report the minimum one.

Sample Input	Output for Sample Input
3 3 1 7 3 9901 1	Case 1: 3 Case 2: 6 Case 3: 12

同余定理：（a+b)%n==(a%n+b%n)%n；

代码：

#include<stdio.h>
#include<string.h>
int main()
{
int T;
int n,m;
int c=1;
scanf("%d",&T);
while(T--)
{
scanf("%d%d",&n,&m);
int a=m%n;
int k=1;
while(a)
{
a=(a*10%n+m%n)%n;
k++;
}
printf("Case %d: %d\n",c++,k);
}
return 0;
}