Problem:
Score : 400 points

Problem Statement

You are given integers N and M.

Consider a sequence a of length N consisting of positive integers such that a_1 + a_2 + ... + a_N = M. Find the maximum possible value of the greatest common divisor of a_1, a_2, ..., a_N.

Constraints

All values in input are integers.

1 \leq N \leq 10^5

N \leq M \leq 10^9

Input

Input is given from Standard Input in the following format:

N M

Output

Print the maximum possible value of the greatest common divisor of a sequence a_1, a_2, ..., a_N that satisfies the condition.

Sample Input 1

3 14

Sample Output 1

2

Consider the sequence (a_1, a_2, a_3) = (2, 4, 8). Their greatest common divisor is 2, and this is the maximum value.

Sample Input 2

10 123

Sample Output 2

3

Sample Input 3

100000 1000000000

Sample Output 3

10000

Solution in C (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>

int main(){
  int N,M;
  scanf("%d%d",&N,&M);

  int gcd=1;
  int p;//探索範囲
  p=M/N;
  int a=1;

  while(p>=2){
    a=1;
    for(int i=p;i>=2;i--){
      if(M%i==0){
        M=M/i;
        gcd=gcd*i;
        p=M/N;
        a=0;
        break;
      }
    }
    if(a==1) break;
  }

  printf("%d\n",gcd);
  return 0;
}