#include<iostream>
#include<cstdio>
#include<cmath>
#include<cstdlib>
#include<cstring>
#include<algorithm>
#include<queue>
#include<map>
#include<bitset>
using namespace std;
#define ll long long
#define N 50010
#define P 1000000007
char getc(){char c=getchar();while (c==10||c==13||c==32) c=getchar();return c;}
int gcd(int n,int m){return m==0?n:gcd(m,n%m);}
int read()
{int x=0,f=1;char c=getchar();while (c<'0'||c>'9') {if (c=='-') f=-1;c=getchar();}while (c>='0'&&c<='9') x=(x<<1)+(x<<3)+(c^48),c=getchar();return x*f;
}
int n,m,S,T,t,p[N],f[2][N],g[N];
ll d[2][N];
bool flag[N];
struct data{int to,nxt,len;
}edge[N<<1];
struct data2
{int x;ll d;bool operator <(const data2&a) const{return d>a.d;}
};
priority_queue<data2> q;
bitset<N> to[N],from[N];
map<int,bitset<N> > cnt;
void addedge(int x,int y,int z){t++;edge[t].to=y,edge[t].nxt=p[x],edge[t].len=z,p[x]=t;}
void inc(int &x,int y){x+=y;if (x>=P) x-=P;}
void dijkstra(int S,int op)
{memset(d[op],42,sizeof(d[op]));d[op][S]=0;f[op][S]=1;memset(flag,0,sizeof(flag));while (!q.empty()) q.pop();q.push((data2){S,0});for (;;){while (!q.empty()&&flag[q.top().x]) q.pop();if (q.empty()) break;data2 x=q.top();q.pop();flag[x.x]=1;for (int i=p[x.x];i;i=edge[i].nxt){if (x.d+edge[i].len<d[op][edge[i].to]){d[op][edge[i].to]=x.d+edge[i].len;q.push((data2){edge[i].to,d[op][edge[i].to]});f[op][edge[i].to]=0;}if (x.d+edge[i].len==d[op][edge[i].to])inc(f[op][edge[i].to],f[op][x.x]);}}
}
namespace shortestpathDAG
{int p[N]={0},q[N]={0},degree[N]={0},t=0;struct data{int to,nxt;}edge[N];void addedge(int x,int y){t++;edge[t].to=y,edge[t].nxt=p[x],p[x]=t;}void topsort(){for (int i=1;i<=t;i++) degree[edge[i].to]++;int head=0,tail=0;for (int i=1;i<=n;i++) if (!degree[i]) q[++tail]=i;while (tail<n){int x=q[++head];for (int i=p[x];i;i=edge[i].nxt){degree[edge[i].to]--;if (!degree[edge[i].to]) q[++tail]=edge[i].to;}}}void work(){ll ans=0;for (int i=1;i<=n;i++){int x=q[i];from[x][x]=1;for (int j=p[x];j;j=edge[j].nxt)from[edge[j].to]|=from[x];}for (int i=n;i>=1;i--){int x=q[i];to[x][x]=1;for (int j=p[x];j;j=edge[j].nxt)to[x]|=to[edge[j].to];ans+=((~(to[x]|from[x]))&cnt[(g[T]-g[x]+P)%P]).count();}cout<<(ans>>1);}
}
int main()
{
#ifndef ONLINE_JUDGEfreopen("bzoj5109.in","r",stdin);freopen("bzoj5109.out","w",stdout);const char LL[]="%I64d\n";
#elseconst char LL[]="%lld\n";
#endifn=read(),m=read(),S=read(),T=read();for (int i=1;i<=m;i++){int x=read(),y=read(),z=read();addedge(x,y,z),addedge(y,x,z);}dijkstra(S,0),dijkstra(T,1);if (f[0][T]==0) {cout<<(1ll*n*(n-1)>>1);return 0;}for (int i=1;i<=n;i++){if (d[0][i]+d[1][i]==d[0][T]) g[i]=1ll*f[0][i]*f[1][i]%P;cnt[g[i]][i]=1;}for (int i=1;i<=t;i+=2){if (d[0][edge[i+1].to]+d[1][edge[i].to]+edge[i].len==d[0][T]) shortestpathDAG::addedge(edge[i+1].to,edge[i].to);if (d[0][edge[i].to]+d[1][edge[i+1].to]+edge[i].len==d[0][T]) shortestpathDAG::addedge(edge[i].to,edge[i+1].to);}shortestpathDAG::topsort();shortestpathDAG::work();return 0;
}