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 Int = long long;
//INSERT ABOVE HERE
signed main(){
  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;
    a--;b--;
    G[a].emplace_back(b);
    G[b].emplace_back(a);
  }
  using P = pair<Int, Int>;
  vector<vector<Int> > dp(2,vector<Int>(n,-1)); 
  queue<P> q;
  q.emplace(0,s);
  dp[0][s]=0;
  while(!q.empty()){
    Int d,v;
    tie(d,v)=q.front();q.pop();
    for(Int u:G[v]){
      Int nd=d+1;
      if(~dp[nd&1][u]) continue;
      dp[nd&1][u]=nd;
      q.emplace(nd,u);
    }
  }

  if(dp[0][t]==2){
    cout<<2<<endl;
    return 0;
  }

  if(dp[1][t]<0){
    cout<<-1<<endl;
    return 0;
  }

  auto isp=[](Int x){
	     if(x<2) return false;
	     for(Int i=2;i*i<=x;i++)
	       if(x%i==0) return false;
	     return true;
	   };

  Int ans=dp[1][t];
  while(!isp(ans)) ans+=2;
  cout<<ans<<endl;
  
  return 0;
}