#include <bits/stdc++.h>

#define forn(i, n) for(int i = 0; i < (int)n; ++i)
#define for1(i, n) for(int i = 1; i <= (int)n; ++i)
#define fore(i, l, r) for(int i = (int)l; i <= (int)r; ++i)
#define all(x) x.begin(), x.end()
#define el '\n'
#define d(x) cerr << #x << ' ' << x << el

#define sz(a) (int) a.size()
#define pb push_back
using namespace std;

typedef long long ll;
typedef vector<int> vi;
typedef array<int, 4> a4;
typedef pair<int,int> ii;
typedef tuple<ll,int,int> iii;
const int nax = 2e5;
// const int nax = 2e3;
vi g[nax];
ll dist[3][nax];
int visited[3][nax];
const ll inf = 1e17;
void solve(){
    int n,m,k,d;
    cin>>n>>m>>k>>d;
    --k;
    forn(i,m){
        int u,v;
        cin>>u>>v;
        --u,--v;
        g[u].pb(v), g[v].pb(u);
    }

    queue<ii> q;
    q.push({n-1, d});
    dist[0][n-1] = d;
    visited[0][n-1]= 1;
    while(!q.empty()){
        int siz = sz(q);
        while(siz--){
            auto [u, mod]= q.front();
            q.pop();
            ll curDist = dist[0][u];
            for(int v : g[u]){
                if(!visited[0][v])
                {
                    visited[0][v] = 1;
                    int newMod = (mod - 1 + d) % d;
                    if(!newMod) newMod = d;
                    dist[0][v] = curDist + newMod;
                    q.push({v, newMod});
                }
            }
        }
    }
    queue<int> q1;
    q1.push(k);
    visited[1][k] = 1;
    dist[1][k] = 0;
     while(!q1.empty()){
        int siz = sz(q1);
        while(siz--){
            auto u = q1.front();
            q1.pop();
            ll curDist = dist[1][u];
            for(int v : g[u]){
                if(!visited[1][v])
                {
                    visited[1][v] = 1;
                    dist[1][v] = curDist + 1;
                    q1.push(v);
                }
            }
        }
    }



    priority_queue<pair<ll,int>, vector<pair<ll,int>>, greater<pair<ll,int>>> pq;
    pq.push({0,0});
    vector<ll> curDist(n, inf);
    curDist[0] = 0;
    ll ans = inf;
    while(!pq.empty()){
        int siz = sz(pq);
        while(siz--){
            auto [distU, u] = pq.top();
            // d(distU), d(u), d(same);
            pq.pop();
            if(distU > curDist[u]) continue;

            for(int v : g[u]){
                bool joined = dist[1][v] >= d;//dist al K
                if(joined){
                    ans = min(ans, distU + dist[0][v]);
                }else{
                    if(curDist[v] > distU + d - dist[1][v]){
                        curDist[v] = distU + d - dist[1][v];
                        pq.push({curDist[v], v});
                    }
                }
            }
        }
    }

    cout<<ans<<el;

  
    // ll ans = min(curDist[0][n-1], curDist[1][n-1]);
    // cout<<ans<<el;
}
int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    int tt = 1;
    // cin>>tt;
    while(tt--){
        solve();
    }
}