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 <bits/stdc++.h>
using namespace std;

constexpr int inf = 1e9;

using pii = pair<int, int>;

int main() {
    const int max_v = 1e6;
    vector<bool> is_prime(max_v, true);
    vector<int> ps;
    is_prime[0] = is_prime[1] = false;
    for(int i = 2; i < max_v; ++i) {
        if(is_prime[i]) {
            ps.push_back(i);
            for(int j = i + i; j < max_v; j += i) {
                is_prime[j] = false;
            }
        }
    }

    int n, m, s, t; cin >> n >> m >> s >> t;
    s--, t--;
    vector<vector<int>> g(n);
    for(int i = 0; i < m; ++i) {
        int a, b; cin >> a >> b;
        g[a - 1].push_back(b - 1);
        g[b - 1].push_back(a - 1);
    }

    vector<vector<int>> d(n, vector<int>(2, inf));
    d[s][0] = 0;
    queue<pii> que;
    que.emplace(s, 0);
    while(!que.empty()) {
        auto now = que.front(); que.pop();
        const int v = now.first, pari = now.second;
        for(auto to : g[v]) {
            if(d[to][!pari] > d[v][pari] + 1) {
                d[to][!pari] = d[v][pari] + 1;
                que.emplace(to, !pari);
            }
        }
    }
    if(d[t][0] == 2) {
        cout << 2 << endl;
    } else {
        if(d[t][1] == inf) {
            cout << -1 << endl;
        } else if(d[t][1] == 1) {
            cout << 3 << endl;
        } else {
            cout << *lower_bound(begin(ps), end(ps), d[t][1]) << endl;
        }
    }
}