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;
int INF = 10000000;
bool is_prime(int n){
  if (n == 1){
    return false;
  }
  for (int i = 2; i * i <= n; i++){
    if (n % i == 0){
      return false;
    }
  }
  return true;
}
int main(){
  int N, M, S, T;
  cin >> N >> M >> S >> T;
  S--;
  T--;
  vector<vector<int>> E(N * 2);
  for (int i = 0; i < M; i++){
    int a, b;
    cin >> a >> b;
    a--;
    b--;
    E[a * 2].push_back(b * 2 + 1);
    E[a * 2 + 1].push_back(b * 2);
    E[b * 2].push_back(a * 2 + 1);
    E[b * 2 + 1].push_back(a * 2);
  }
  vector<int> d(N * 2, INF);
  d[S * 2] = 0;
  queue<int> Q;
  Q.push(S * 2);
  while (!Q.empty()){
    int v = Q.front();
    Q.pop();
    for (int w : E[v]){
      if (d[w] == INF){
        d[w] = d[v] + 1;
        Q.push(w);
      }
    }
  }
  if (d[T * 2] == 2){
    cout << 2 << endl;
  } else if (d[T * 2 + 1] == INF){
    cout << -1 << endl;
  } else {
    int p = d[T * 2 + 1];
    while (!is_prime(p)){
      p += 2;
    }
    cout << p << endl;
  }
}