Problem: Fox Jiro is one of the staffs of the ACM-ICPC 2018 Asia Yokohama Regional Contest and is responsible for designing the network for the venue of the contest. His network consists of $N$ computers, which are connected by $M$ cables. The $i$-th cable connects the $a_i$-th computer and the $b_i$-th computer, and it carries data in both directions. Your team will use the $S$-th computer in the contest, and a judge server is the $T$-th computer.

He decided to adjust the routing algorithm of the network to maximize the performance of the contestants through the magical power of prime numbers. In this algorithm, a packet (a unit of data carried by the network) is sent from your computer to the judge server passing through the cables a prime number of times if possible. If it is impossible, the contestants cannot benefit by the magical power of prime numbers. To accomplish this target, a packet is allowed to pass through the same cable multiple times.

You decided to write a program to calculate the minimum number of times a packet from $S$ to $T$ needed to pass through the cables. If the number of times a packet passes through the cables cannot be a prime number, print $-1$.



Input

The input consists of a single test case, formatted as follows.


$N$ $M$ $S$ $T$
$a_1$ $b_1$
$\vdots$
$a_M$ $b_M$


The first line consists of four integers $N, M, S,$ and $T$ ($2 \leq N \leq 10^5, 1 \leq M \leq 10^5, 1 \leq S, T \leq N, S \ne T$). The $i$-th line of the following $M$ lines consists of two integers $a_i$ and $b_i$ ($1 \leq a_i < b_i \leq N$), which means the $i$-th cables connects the $a_i$-th computer and the $b_i$-th computer in the network. You can assume that the network satisfies the following conditions.

* The network has no multi-edge, i.e.,$(a_i, b_i) \ne (a_j, b_j)$ for all $i,j$ ($1 \leq i < j \leq M$).
* The packets from $N$ computers are reachable to $T$ by passing through some number of cables. The number is not necessarily a prime.

Output

If there are ways such that the number of times a packet sent from $S$ to $T$ passes through the cables is a prime number, print the minimum prime number of times in one line. Otherwise, print $-1$.

Examples

Input

5 5 1 5
1 2
1 4
2 3
3 4
3 5


Output

3


Input

5 4 1 5
1 2
2 3
3 4
4 5


Output

-1


Input

2 1 1 2
1 2


Output

3


Input

3 3 1 2
1 2
1 3
2 3


Output

2

Solution (in CPP):

Solution:
#include <iostream>
#include <vector>
#include <algorithm>
#include <queue>
#include <utility>
using namespace std;
const int inf = 1e9;
typedef pair<int, int> pii;

int main(){
	vector<bool> prime(1000000, true);
	prime[0] = prime[1] = false;
	for(int i=2; i*i <1000000; i++){
		if(prime[i]){
			for(int j=i*2; j<1000000; j+=i){
				prime[j] = false;
			}
		}
	}

	int n,m,s,t;
	cin >> n >> m >> s >> t;
	s--; t--;
	vector<vector<int>> adj(n);
	for(int i=0; i<m; i++){
		int a,b;
		cin >> a >> b;
		a--; b--;
		adj[a].push_back(b);
		adj[b].push_back(a);
	}

	queue<pii> wait;
	wait.push(pii(s, 0));
	vector<vector<int>> mincost(n, vector<int>(2, inf));
	mincost[s][0] = 0;
	while(!wait.empty()){
		pii curr = wait.front();
		wait.pop();
		for(int next: adj[curr.first]){
			if(mincost[next][1-curr.second] == inf){
				mincost[next][1-curr.second] = mincost[curr.first][curr.second]+1;
				wait.push(pii(next, 1-curr.second));
			}
		}
	}

	if(mincost[t][0] == 2){
		cout << 2 << endl;
		return 0;
	}
	if(mincost[t][1] == inf){
		cout << -1 << endl;
		return 0;
	}
	for(int i=mincost[t][1]; ; i+=2){
		if(prime[i]){
			cout << i << endl;
			break;
		}
	}
	return 0;
}