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;

using int64 = long long;

int main() {
  int N, M, S, T;
  vector< int > g[100000];

  cin >> N >> M >> S >> T;
  --S, --T;
  for(int i = 0; i < M; i++) {
    int x, y;
    cin >> x >> y;
    --x, --y;
    g[x].push_back(y);
    g[y].push_back(x);
  }

  int d[100000][2];
  memset(d, -1, sizeof(d));
  queue< pair< int, pair< int, int>> > que;
  que.emplace(0, make_pair(S, 0));
  d[S][0] = 0;
  while(que.size()) {
    int cost = que.front().first;
    auto p = que.front().second;
    que.pop();
    for(auto &to : g[p.first]) {
      if(d[to][p.second ^ 1] == -1) {
        d[to][p.second ^ 1] = cost + 1;
        que.emplace(cost + 1, make_pair(to, p.second ^ 1));
      }
    }
  }

  if(d[T][0] == 2) {
    cout << 2 << endl;
    return 0;
  }

  if(d[T][1] == -1) {
    cout << -1 << endl;
    return 0;
  }

  bool primes[1010101] = {};
  for(int i = 2; i < 1010101; i++) {
    if(primes[i]) continue;
    if(d[T][1] <= i && i >= 3) {
      cout << i << endl;
      return 0;
    }
    for(int j = i + i; j < 1010101; j += i) {
      primes[j] = true;
    }
  }
}