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++14 (GCC 5.4.1) (judge verdict: Accepted)

#define _CRT_SECURE_NO_WARNINGS
#define MATH_PI 3.14159265358979323846264338327950288419716939
#define DIVIDER9 1000000007
#define lli long long int
#include <iostream>
#include <string.h>
#include <fstream>
#include <math.h>
#include <iomanip>

using namespace std;

#ifdef _WIN32
#pragma warning(disable : 4101)


signed wait(){
	char wait_dummy[256];
	scanf("%c", &wait_dummy);
	return 0;
}


template <typename ... Args>
void dout(const char *format, Args const & ... args){
	printf(format, args ...);
}

#define MAX_CHARBUF	65536
#define DATAFILE "data.dat"

class csLocalInput{
	int FileOpen();
public:
	FILE *fp;
	csLocalInput();
};


csLocalInput::csLocalInput() {
	FileOpen();
}

int csLocalInput::FileOpen() {
	fp = fopen(DATAFILE, "rt");
	return 1;
}

csLocalInput local_in;


#define DEBUG	1
#else
inline signed wait() { return 0; }
inline void dout(const char *arg, ...) {}
#endif

template<typename T>inline void SWAP(T &a, T &b) { T t = a; a = b; b = t; }
inline void CSWAP(char *&a, char *&b) { char *t = a; a = b; b = t; }

int _ret;

#define CLIP(ptr, min, max) {if((min)<=(max)){if(ptr<(min)){ptr=(min);}if(ptr>(max)){ptr=(max);}}}


#define Sin(deg) sin((deg)*MATH_PI/180.0)
#define Cos(deg) cos((deg)*MATH_PI/180.0)
#define Tan(deg) tan((deg)*MATH_PI/180.0)
#define Rad(deg) ((deg)*MATH_PI/180.0)
#define rep(param, num) for(int param=0 ; param<num ; ++param)
#define fi(num) for(int i=0 ; i<num ; ++i)
#define fj(num) for(int j=0 ; j<num ; ++j)
#define fk(num) for(int k=0 ; k<num ; ++k)
#define fl(num) for(int l=0 ; l<num ; ++l)
#define fn(num) for(int n=0 ; n<num ; ++n)
#define ffr(param, num) for(int param=num-1 ; param>=0 ; --param)
#define fir(num) for(int i=num-1 ; i>=0 ; --i)
#define fjr(num) for(int j=num-1 ; j>=0 ; --j)
#define fkr(num) for(int k=num-1 ; k>=0 ; --k)
#define flr(num) for(int l=num-1 ; l>=0 ; --l)
#define fnr(num) for(int n=num-1 ; n>=0 ; --n)
#define gi(p) int p; Gi(p)
#define gi2(p1, p2) int p1, p2; Gi2(p1, p2)
#define gi3(p1, p2, p3) int p1, p2, p3; Gi3(p1, p2, p3)
#define gi4(p1, p2, p3, p4) int p1, p2, p3, p4; Gi4(p1, p2, p3, p4)
#define glli(p) lli p; Glli(p)
#define glli2(p1, p2) lli p1, p2; Glli2(p1, p2)
#define glli3(p1, p2, p3) lli p1, p2, p3; Glli3(p1, p2, p3)
#define glli4(p1, p2, p3, p4) lli p1, p2, p3, p4; Glli4(p1, p2, p3, p4)
#define gf(p) double p; Gf(p);
#define gf2(p1, p2) double p1, p2; Gf2(p1, p2);
#define gf3(p1, p2, p3) double p1, p2, p3; Gf3(p1, p2, p3);
#define gf4(p1, p2, p3, p4) double p1, p2, p3, p4; Gf4(p1, p2, p3, p4)

#define Gi(p) _ret = Scanf("%d", p)
#define Gi2(p1, p2) _ret = Scanf2("%d %d", p1, p2)
#define Gi3(p1, p2, p3) _ret = Scanf3("%d %d %d", p1, p2, p3)
#define Gi4(p1, p2, p3, p4) _ret = Scanf4("%d %d %d %d", p1, p2, p3, p4)
#define Glli(p) _ret = Scanf("%lld", p)
#define Glli2(p1, p2) _ret = Scanf2("%lld %lld", p1, p2)
#define Glli3(p1, p2, p3) _ret = Scanf3("%lld %lld %lld", p1, p2, p3)
#define Glli4(p1, p2, p3, p4) _ret = Scanf4("%lld %lld %lld %lld", p1, p2, p3, p4)
#define Gf(p) _ret = Scanf("%f", p)
#define Gf2(p1, p2) _ret = Scanf2("%f %f", p1, p2)
#define Gf3(p1, p2, p3) _ret = Scanf3("%f %f %f", p1, p2, p3)
#define Gf4(p1, p2, p3, p4) _ret = Scanf4("%f %f %f %f", p1, p2, p3, p4)

#ifdef DEBUG
#define Gc(buf) fscanf(local_in.fp, "%s", buf)
#define Scanf(expr, p) fscanf(local_in.fp, expr, &p)
#define Scanf2(expr, p1, p2) fscanf(local_in.fp, expr, &p1, &p2)
#define Scanf3(expr, p1, p2, p3) fscanf(local_in.fp, expr, &p1, &p2, &p3)
#define Scanf4(expr, p1, p2, p3, p4) fscanf(local_in.fp, expr, &p1, &p2, &p3, &p4)
#else
#define Gc(buf) Scanf("%s", buf)
#define Scanf(expr, p) scanf(expr, &p)
#define Scanf2(expr, p1, p2) scanf(expr, &p1, &p2)
#define Scanf3(expr, p1, p2, p3) scanf(expr, &p1, &p2, &p3)
#define Scanf4(expr, p1, p2, p3, p4) scanf(expr, &p1, &p2, &p3, &p4)
#endif
#define ans(p) cout << p << endl;
#define ans_end(p) {cout << p << endl; return wait();}
void CombSort(int N, int *ar, int order_ascending) { if (N <= 1) return; int h = int(N / 1.3); int flag; int i; while (true) { flag = 0; for (i = 0; i + h < N; ++i) { if ((order_ascending&&ar[i] > ar[i + h]) || (!order_ascending&&ar[i] < ar[i + h])) { swap<int>(ar[i], ar[i + h]); flag = 1; } }if (h == 1 && !flag)break; if (h == 9 || h == 10) h = 11; if (h > 1)h = int(h / 1.3); } }
void CombSort_ll(int N, lli *ar, int order_ascending) { if (N <= 1) return; int h = int(N / 1.3); int flag; int i; while (true) { flag = 0; for (i = 0; i + h < N; ++i) { if ((order_ascending&&ar[i] > ar[i + h]) || (!order_ascending&&ar[i] < ar[i + h])) { swap<lli>(ar[i], ar[i + h]); flag = 1; } }if (h == 1 && !flag)break; if (h == 9 || h == 10) h = 11; if (h > 1)h = int(h / 1.3); } }

int EuclideanAlgorithm(int N, int *ar){
	fn(N - 1){
		while (true){ 
			if (ar[n] % ar[n + 1] == 0 || ar[n + 1] % ar[n] == 0) {
				ar[n + 1] = ar[n] < ar[n + 1] ? ar[n] : ar[n + 1];
				break; 
			}
			if (ar[n] > ar[n + 1]) {
				ar[n] %= ar[n + 1];
			} 
			else { 
				ar[n + 1] %= ar[n]; 
			} 
		} 
	}
	return ar[N - 1];
}

template<typename T>void CombSort(int N, T *ar, int order_ascending) {
	if (N <= 1) return;
	int i, flag;
	int h = int(N / 1.3);
	while (true) {
		flag = 0;
		for (i = 0; i + h < N; ++i) {
			if (
				order_ascending && ar[i].SortValue > ar[i + h].SortValue ||
				!order_ascending && ar[i].SortValue < ar[i + h].SortValue
				) {
				SWAP<T>(ar[i], ar[i + h]);
				flag = 1;
			}
		}
		if (h > 1) {
			h = int(h / 1.3);
			if (h == 9 || h == 10) h = 11;
		}
		else {
			if (!flag) break;
		}
	}
}
#include <vector>
#include <algorithm>

struct UnionFind {
	vector<int> par; 

	UnionFind(int N) : par(N) { 
		for (int i = 0; i < N; i++) par[i] = i;
	}

	int root(int x) { 
		if (par[x] == x) return x;
		return par[x] = root(par[x]);
	}

	void unite(int x, int y) { 
		int rx = root(x); 
		int ry = root(y); 
		if (rx == ry) return; 
		par[rx] = ry; 
	}

	bool same(int x, int y) { 
		int rx = root(x);
		int ry = root(y);
		return rx == ry;
	}
};


void Replace(char *c, int len, char before, char after) {
	fi(len){
		if(c[i] == before) c[i] = after;
	}
}
void Replace(char *c, char before, char after){
	int len = strlen(c);
	Replace(c, len, before, after);
}

class csNode{
public:
	csNode(){
	}

};

class csStack{
public:
	csStack(){
		num = 0;
	}
	void alloc(int size){
		param = new int[size];
	}
	void sort(int order = 1){
		if(num > 1) CombSort(num, param, order);
	}

	int num;
	int *param;

	void push(int p){
		param[num++] = p;
	}
};

class csPosition{
public:
	csPosition(){x = y = 0;}
	int x, y;
};
typedef class csPosition POS;

template<typename T>
class csPos{
public:
	csPos(){x = y = 0;}
	T x, y;
};

char s[200010];


signed main() {

	gi2(n, m);

	if(n == 1) ans_end(m);

	int mx = 1;
	int N = sqrt(m) + 1;
	int p, d;
	int i;
	for(i=2 ; i<=N ; ++i){
		if(m % i == 0){
			p = m / i;
			d = m / p;
			if(d >= n) ans_end(p);
		}
	}

	for (i = 2; i <= N; ++i) {
		if (m % i == 0) {
			d = m / i;
			p = m / d;
			if (d >= n){
				mx = max(mx, i);
			}
		}
	}

	ans(mx);

	return wait();
}