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;
#define r(i,n) for(int i=0;i<n;i++)
typedef pair<int,int>P;
 
int dp[100009][2];
int c[100009];
vector<int>v[100009];
bool so[2000009];
bool used[100009][2];
 
 
int main(){
 
  so[0]=so[1]=1;
 
  for(int i=2;i<=2000000;i++)if(!so[i]){
    for(int j=i+i;j<=2000000;j+=i) so[j]=1;
  }
 
 
  int n,m,s,t;
  cin>>n>>m>>s>>t;s--;t--;
  r(i,m){
    int a,b;
    cin>>a>>b;
    a--;b--;
    v[a].push_back(b);
    v[b].push_back(a);
  }
 
  queue<P>q;
  q.push(P(s,0));
  used[s][0]=1;
  while(!q.empty()){
    int x=q.front().first;
    int y=q.front().second;q.pop();
    r(i,v[x].size()){
      int nex=v[x][i];
      int cost=dp[x][y]+1;
      if(!used[nex][cost%2]){
        used[nex][cost%2]=1;
        dp[nex][cost%2]=cost;
        q.push(P(nex,cost%2));
      }
    }
  }
  if(dp[t][0]==2)cout<<2<<endl;
  else if(!used[t][1])cout<<-1<<endl;
  else{
    while(so[dp[t][1]])dp[t][1]+=2;
    cout<<dp[t][1]<<endl;
  }
}