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: Time Limit Exceeded)

#include <stdio.h>

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

  int a[100000];
  int pos=0;
  for(int i = 1; i <= M; i++) {
    if(M % i == 0) {
      a[pos+0] = i;
      a[pos+1] = M / i;
      pos+=2;

      if(a[pos-1] <= (i+1)) break;
    }
  }

  int H = M / N;
  int max = 0;
  for(int i = 0; i < pos; i++) {
    if(a[i] <= H && a[i] > max) {
      max = a[i];
    }
  }
  printf("%d\n", max);

  return 0;
}