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:
#define  _CRT_SECURE_NO_WARNINGS
#pragma comment (linker, "/STACK:526000000")

#include "bits/stdc++.h"

using namespace std;
typedef string::const_iterator State;
#define eps 1e-11L
#define MAX_MOD 1000000007LL
#define GYAKU 500000004LL

#define MOD 998244353LL
#define seg_size 262144 * 4LL
#define pb push_back
#define mp make_pair
typedef long long ll;
#define REP(a,b) for(long long (a) = 0;(a) < (b);++(a))
#define ALL(x) (x).begin(),(x).end()

void init() {
	iostream::sync_with_stdio(false);
	cout << fixed << setprecision(20);
}

#define int ll
vector<int> vertexs[100001];
int dp[2][100001];
void solve(){
	int n, m, s, t;
	cin >> n >> m >> s >> t;
	REP(i, m) {
		int a, b;
		cin >> a >> b;
		vertexs[a].push_back(b);
		vertexs[b].push_back(a);
	}
	REP(i, n) {
		dp[0][i+1] = 1e9;
		dp[1][i + 1] = 1e9;
	}
	dp[0][s] = 0;
	queue<pair<int, int>> next;
	next.push(mp(0, s));
	while (next.empty() == false) {
		pair<int, int> now = next.front();
		next.pop();
		for (auto x : vertexs[now.second]) {
			if (dp[(now.first + 1) % 2][x] > now.first + 1) {
				dp[(now.first + 1) % 2][x] = now.first + 1;
				next.push(mp((now.first + 1), x));
			}
		}
	}
	int ans = 1e9;
	if (dp[0][t] == 2) {
		cout << 2 << endl;
		return;
	}
	if (dp[1][t] == 1e9) {
		cout << -1 << endl;
		return;
	}
	for (int i = max(3LL, dp[1][t]);;i += 2) {
		int ok = 1;
		for (int q = 2; q * q <= i; ++q) {
			if (i % q == 0) ok = 0;
		}
		if (ok == 1) {
			cout << i << endl;
			return;
		}
	}
}

#undef int
int main() {
	init();
	solve();
}