/*
cat <<EOF >mistaken-paste
*/

#pragma GCC diagnostic ignored "-Wincompatible-pointer-types"

#include <stdio.h>
#include <stdint.h>
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>
#include <math.h>

#define BIG 2000000007
#define VERYBIG 200000000000007LL

#define MOD 1000000007
typedef uint64_t ull;
typedef  int64_t sll;

#define N_MAX 100000
#define M_MAX 200000

#ifdef __cplusplus
#include <queue>
#include <stack>
// #include <tuple>

using namespace std; // I'm NOT gonna use C++ without compro. shit

typedef priority_queue<ull, vector<ull>, greater<ull> > upque123;
typedef priority_queue<ull, vector<ull> > upque321;
typedef priority_queue<sll, vector<sll>, greater<sll> > spque123;
typedef priority_queue<sll, vector<sll> > spque321;

#endif

typedef struct {
	int32_t a;
	int32_t b;
} hw;

typedef struct {
	sll a;
	sll b;
} hwll;

typedef struct {
	hwll a;
	hwll b;
} linell;


typedef struct {
	ull s;
	ull t;
	int32_t c;
} struct_a;

typedef struct {
	int32_t from;
	int32_t to;
	sll cost;
} struct_b;



const hw vector8[8] = {
	{-1, -1},
	{-1,  0},
	{-1, +1},
	{ 0, -1},
	{ 0, +1},
	{+1, -1},
	{+1,  0},
	{+1, +1}
};

ull n, m;
ull h, w;
ull k;
ull q;
ull vua, vub, vuc, vud, vue, vuf;
sll vsa, vsb, vsc, vsd, vse, vsf;
long double vra, vrb, vrc;
double vda, vdb, vdc;
size_t slen;
size_t tlen;
char ch, dh;

void swap_adj (ull *a, ull *b) {
	if (*a != *b) {
		ull tmp = *b;
		*b = *a;
		*a = tmp;
	}
	return;
}

int32_t digits (ull x) {
	int32_t i = 1;
	while (x >= 10) {
		x /= 10;
		i++;
	}
	return i;
}

ull umin (ull x, ull y) {
	return (x < y) ? x : y;
}

ull umax (ull x, ull y) {
	return (x > y) ? x : y;
}

sll smin (sll x, sll y) {
	return (x < y) ? x : y;
}

sll smax (sll x, sll y) {
	return (x > y) ? x : y;
}

ull gcd (ull x, ull y) {
	if (x < y) {
		return gcd(y, x);
	} else if (y == 0) {
		return x;
	} else {
		return gcd(y, x % y);
	}
}

ull bitpow (ull a, ull x, ull modulo) {
	ull result = 1;
	while (x) {
		if (x & 1) {
			result *= a;
			result %= modulo;
		}
		x /= 2;
		a = (a * a) % modulo;
	}
	return result;
}

ull divide (ull a, ull b, ull modulo) {
	return (a * bitpow(b, modulo - 2, modulo)) % modulo;
}

ull ullabs (ull a, ull b) {
	if (a >= b) {
		return a - b;
	} else {
		return b - a;
	}
}

sll sllabs (sll a, sll b) {
	if (a >= b) {
		return a - b;
	} else {
		return b - a;
	}
}

sll nibutanlobo (bool (*func)(sll arg), sll ok, sll ng) {
	while (sllabs(ok, ng) > 1) {
		sll med = (ok + ng) / 2;
		if (func(med)) {
			ok = med;
		} else {
			ng = med;
		}

		// printf("debug: [%lld %lld)\n", ok, ng);
	}

	if (!func(ok)) return ok * 2 - ng;
	return ok;
}

void printUquotient (ull left, ull right) {
	const int32_t digits = 20;

	printf("%llu.", left / right);
	left %= right;
	for (int32_t i = 0; i < digits; i++) {
		left *= 10;
		printf("%1d", left / right);
		left %= right;
	}
	puts("");

	return;
}

void printSquotient (sll left, sll right) {
	if (left * right < 0) putchar('-');
	printUquotient(sllabs(left, 0), sllabs(right, 0));

	return;
}

int bitcount (ull n) {
	int result = 0;
	while (n) {
		if (n & 1) result++;
		n /= 2;
	}
	return result;
}

#ifdef __cplusplus

typedef struct {
	int32_t to;
	sll cost;
} edge;
typedef pair<sll, int32_t> P;

std::vector<edge> g[N_MAX];
void dijk_init (ull n, struct_b arr[]) {
	edge x;
	for (int32_t i = 0; i < n; i++) {
		x.to = arr[i].to;
		x.cost = arr[i].cost;
		g[arr[i].from].push_back(x);
	}
}

void dijk_distinit (int s, sll distance[], ull n) {
	for (int32_t i = 0; i < n; i++) {
		distance[i] = VERYBIG;
	}
	distance[s] = 0;
	return;
}

bool dijkstra (int s, sll distance[]) {
	priority_queue<P, std::vector<P>, greater<P> > que; // (最短距離, 頂点番号)
	que.push(P(distance[s], s));

	bool ischanged = false;
	while (!que.empty()) {
		P p = que.top();
		que.pop();

		sll v = p.second;
		if (distance[v] < p.first) continue;

		int32_t maxsize = g[v].size();
		for (int32_t i = 0; i < maxsize; i++) {
			edge e = g[v][i];
			if (distance[e.to] > distance[v] + e.cost) {
				distance[e.to] = distance[v] + e.cost;
				ischanged = true;
				que.push(P(distance[e.to], e.to));
			}
		}
	}

	return ischanged;
}

void dijkstra_kaizo (int s, sll distance[], ull ways[]) {
	priority_queue<P, std::vector<P>, greater<P> > que; // (最短距離, 頂点番号)
	que.push(P(distance[s], s));

	while (!que.empty()) {
		P p = que.top();
		que.pop();

		sll v = p.second;
		if (distance[v] < p.first) continue;

		int32_t maxsize = g[v].size();
		for (int32_t i = 0; i < maxsize; i++) {
			edge e = g[v][i];
			if (distance[e.to] > distance[v] + e.cost) {
				distance[e.to] = distance[v] + e.cost;
				que.push(P(distance[e.to], e.to));

				ways[e.to] = ways[v];
			} else if (distance[e.to] == distance[v] + e.cost) {
				ways[e.to] = (ways[e.to] + ways[v]) % MOD;
			}
		}
	}

	return;
}

#endif

// sll dist[N_MAX];
struct_b path[M_MAX * 2];

// ull a[N_MAX];
ull a[M_MAX];
// sll a[N_MAX];
// ull a[N_MAX][N_MAX];
// sll a[N_MAX][N_MAX];
// ull b[N_MAX];
ull b[M_MAX];
// sll b[N_MAX];
// ull c[N_MAX];
sll c[M_MAX];
// char c[N_MAX];
// char s[N_MAX + 1];
// char s[N_MAX + 1][N_MAX + 1];
// char s[N_MAX + 1][M_MAX + 1];
// char t[N_MAX + 1];

// ull alphabets[26];
// char alphabets[26];

// ull dp[N_MAX + 1];
// sll dp[N_MAX + 1];
// ull dp[N_MAX + 1][N_MAX + 1];
// sll dp[N_MAX + 1][N_MAX + 1];
// bool dp[N_MAX + 1];
// bool dp[N_MAX + 1][N_MAX + 1];
// hwll arr[N_MAX];
hwll arr[M_MAX];

// typedef tuple<sll, int32_t, int32_t> P2d;

sll dist1[N_MAX];
sll dist2[N_MAX];
ull ways1[N_MAX];
ull ways2[N_MAX];



double distance (sll x1, sll y1, sll x2, sll y2) {
	double xdist2, ydist2, origindist, dist;

	xdist2 = (x1 - x2) * (x1 - x2);
	ydist2 = (y1 - y2) * (y1 - y2);
	return sqrt(xdist2 + ydist2);
}

int32_t pullcomp (const void *left, const void *right) {
	ull l = *(ull*)left;
	ull r = *(ull*)right;
	if (l < r) {
		return -1;
	}
	if (l > r) {
		return +1;
	}
	return 0;
}

int32_t phwllABcomp (const void *left, const void *right) {
	hwll l = *(hwll*)left;
	hwll r = *(hwll*)right;
	if (l.a < r.a) {
		return -1;
	}
	if (l.a > r.a) {
		return +1;
	}
	if (l.b < r.b) {
		return -1;
	}
	if (l.b > r.b) {
		return +1;
	}
	return 0;
}

ull solve () {
	sll i, j, ki, l;
	// ull result = 0;
	sll result = 0;
	// double result = 0;
	ull maybe = 0;
	// sll maybe = 0;
	// ull sum = 0;
	sll sum = 0;
	ull item;
	ull *dpcell;
	// 比較関数ぐらい即席で書け

	vua--;
	vub--;

	for (i = 0; i < m; i++) {
		path[i].from = path[i + m].to = a[i];
		path[i].to = path[i + m].from = b[i];
		path[i].cost = path[i + m].cost = c[i];
	}
	dijk_init(m * 2, path);

	dijk_distinit(vua, dist1, n);
	dijk_distinit(vub, dist2, n);

	for (i = 0; i < n; i++) {
		ways1[i] = ways2[i] = 0;
	}
	ways1[vua] = ways2[vub] = 1;

	dijkstra_kaizo(vua, dist1, ways1);
	dijkstra_kaizo(vub, dist2, ways2);

	const ull pathlen = dist1[vub];

	// ull beforesum = 0;
	// ull aftersum = 0;

	ull collisionsum = 0;

	for (i = 0; i < n; i++) {
		if (dist1[i] * 2 == pathlen && dist2[i] * 2 == pathlen) {
			// beforesum = (beforesum + ways1[i]) % MOD;
			// aftersum = (aftersum + ways2[i]) % MOD;
			collisionsum = (collisionsum + bitpow((ways1[i] * ways2[i]) % MOD, 2, MOD)) % MOD;
		}
	}
	for (i = 0; i < m * 2; i++) {
		sll f = path[i].from;
		sll t = path[i].to;
		if (dist1[f] + dist2[t] + path[i].cost == pathlen && dist1[f] * 2 < pathlen && dist2[t] * 2 < pathlen) {
			// beforesum = (beforesum + ways1[path[i].from]) % MOD;
			// aftersum = (aftersum + ways2[path[i].to]) % MOD;
			collisionsum = (collisionsum + bitpow((ways1[f] * ways2[t]) % MOD, 2, MOD)) % MOD;
		}
	}

	result = (MOD + (ways1[vub] * ways2[vua] % MOD) - collisionsum) % MOD;

	printf("%llu\n", result);
	// printf("%.12lf\n", (double)result);
	// puts(s);

	return 0;

	success:
	// puts("YES");
	// puts("Yes");
	// printf("%llu\n", result);
	// puts("0");
	puts("CONTINUE");
	return 0;

	fail:
	// puts("NO");
	// puts("No");
	// puts("0");
	puts("-1");
	// puts("-1 -1 -1");
	// puts("GAMEOVER");
	return 1;
}

int32_t main (void) {
	int32_t i, j;
	int32_t x, y;

	// scanf("%lf%lf", &vda, &vdb);
	// scanf("%lld%lld%lld%lld", &vsa, &vsb, &vsc, &vsd);
	// scanf("%llu%llu", &vua, &vub, &vuc, &vud);
	// scanf("%llu%llu", &h, &w);
	scanf("%llu%llu", &n, &m);
	// scanf("%*llu");
	// scanf("%llu", &k, &m, &n);
	scanf("%llu%llu", &vua, &vub, &vuc, &vud, &vue, &vuf);
	// scanf("%lld", &vsa, &vsb, &vsc);
	// scanf("%s", s);
	// scanf("%s", t);
	// scanf("%llu", &k);
	// for (i = 0; i < n; i++) {
	// 	scanf("%llu", &a[i]);
	// 	// a[i]--;
	// }
	// for (i = 0; i < n; i++) {
	// 	scanf("%llu", &b[i]);
	// }
	// for (i = 0; i < h; i++) {
	// 	scanf("%llu", &a[i]);
	// }

	// for (i = 0; i < w; i++) {
	// 	scanf("%llu", &b[i]);
	// }	
	// for (i = 0; i < m; i++) {
	// 	scanf("%llu", &b[i]);
	// }
	// for (i = 0; i < h; i++) {
	// 	scanf("%s", s[i]);
	// }
	// scanf("%s", t);
	for (i = 0; i < m; i++) {
		scanf("%llu", &a[i]);
		scanf("%llu", &b[i]);
		scanf("%llu", &c[i]);
		// arr[i].a--;
		// arr[i].b--;
		a[i]--;
		b[i]--;
	}
	// for (i = 0; i < n; i++) {
	// 	scanf("%llu%llu", &arr[i].a, &arr[i].b);
	// 	// arr[i].a--;
	// 	// arr[i].b--;
	// }
	// for (i = 0; i < n; i++) {
	// 	for (j = 0; j < n; j++) {
	// 		scanf("%lld", &a[i][j]);
	// 	}
	// }
	// for (i = 0; i < n; i++) {
	// 	scanf("%llu%llu%llu", &a[i], &b[i], &c[i]);
	// }

	// scanf("%llu", &q);
	// scanf("%llu", &k);
	// k--;
	// for (i = 0; i < q; i++) {
	// 	scanf("%llu%llu", &a[i], &b[i]);
	// 	a[i]--;
	// 	b[i]--;
	// 	// solve();
	// }

	// for (i = 0; i < m; i++) {
	// 	scanf("%llu%llu", &arr[i].a, &arr[i].b);
	// 	arr[i].a--;
	// 	arr[i].b--;
	// }
	// for (i = 0; i < n; i++) {
	// 	for (j = 0; j < m; j++) {
	// 		scanf("%llu", &a[i][j]);
	// 		a[i][j]--;
	// 	}
	// }

	solve();

	// for (i = 0; i < m; i++) {
	// 	scanf("%llu%llu%llu", &vua, &vub, &vuc);
	// 	// scanf("%s%s", s, t);
	// 	// scanf("%f%f%f", &vda, &vdb, &vdc);
	// 	// scanf("%s", s);
	// 	solve();
	// }

	// while (scanf("%llu%llu", &n, &k), n + k) {
	// 	for (i = 0; i < n; i++) {
	// 		scanf("%llu", &a[i]);
	// 	}
	// 	solve();
	// }

	return 0;
}


Measured memory_bytes: 30800