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 max(a,b) ((a)>(b)?(a):(b))
#define min(a,b) ((a)<(b)?(a):(b))
#define abs(a) max((a),-(a))

typedef long long LL;
typedef long long ll;
typedef pair<int,int> P;
#define rep(i,n) for(int i=0;i<n;i++)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)

const ll mod=1000000007;
const ll INF=mod*mod;

vector<int> v;
bool isp[200000];
void init(){
  fill(isp+2,isp+200000,true);
  for(int i=3;i<200000;i++){
    if(!isp[i])continue;
    v.push_back(i);
    for(int j=2*i;j<200000;j+=i){
      isp[j]=false;
    }
  }
}
vector<int> G[100000];
int used[100000][2];
int main(){
  init();
  int n,m,s,g;cin>>n>>m>>s>>g;s--;g--;
  rep(i,m){
    int a,b;cin>>a>>b;a--;b--;G[a].push_back(b);G[b].push_back(a);
  }
  queue<int> q;q.push(s);
  int out=1000000;
  int cnt=0;
  while(!q.empty()){
    int t=cnt%2;
    int len=q.size();
    rep(i,len){
      int x=q.front();q.pop();
      used[x][t]=1;
      int l=G[x].size();
      rep(j,l){
        int nex=G[x][j];
        if(used[nex][t^1])continue;
        used[nex][t^1]=true;q.push(nex);
        if(cnt+1==2&&nex==g){
          out=min(out,2);
        }
        if(cnt%2==0&&nex==g){
          int le=lower_bound(v.begin(),v.end(),cnt+1)-v.begin();
          out=min(out,v[le]);
        }
      }
    }
    cnt++;
  }
  if(out==1000000)out=-1;
  cout<<out<<endl;
  return 0;
}