use self::mod_int::ModInt;
use std::collections::BinaryHeap;

const MOD: usize = 1e9 as usize + 7;
const INF: i64 = 1 << 60;

fn main() {
    let (r, w) = (std::io::stdin(), std::io::stdout());
    let mut sc = IO::new(r.lock(), w.lock());
    let n: usize = sc.read();
    let m: usize = sc.read();
    let s = sc.read::<usize>() - 1;
    let t = sc.read::<usize>() - 1;
    let mut graph = vec![vec![]; n];
    for _ in 0..m {
        let u = sc.read::<usize>() - 1;
        let v = sc.read::<usize>() - 1;
        let cost: i64 = sc.read();
        graph[u].push((v, cost));
        graph[v].push((u, cost));
    }

    let (dist_s, c_s) = dijkstra(s, &graph);
    let (dist_t, c_t) = dijkstra(t, &graph);
    let shortest_length = dist_s[t];

    let mut collision = ModInt(0);
    for i in 0..n {
        if dist_s[i] * 2 == shortest_length && dist_t[i] == dist_s[i] {
            collision += c_s[i] * c_t[i] * c_s[i] * c_t[i];
        }
        for &(next, edge_cost) in graph[i].iter() {
            if dist_s[i] + edge_cost != dist_s[next] {
                continue;
            }
            if dist_s[i] + edge_cost + dist_t[next] != shortest_length {
                continue;
            }
            if dist_s[i] * 2 >= shortest_length || dist_t[next] * 2 >= shortest_length {
                continue;
            }

            collision += c_s[i] * c_t[next] * c_s[i] * c_t[next];
        }
    }

    let total = c_s[t] * c_t[s];
    let ans = total - collision;
    println!("{}", ans.0);
}

fn dijkstra(s: usize, graph: &Vec<Vec<(usize, i64)>>) -> (Vec<i64>, Vec<ModInt<usize>>) {
    let n = graph.len();
    let mut dist = vec![INF; n];
    dist[s] = 0;
    let mut heap = BinaryHeap::new();
    heap.push((-dist[s], s));
    while let Some((_, v)) = heap.pop() {
        for &(next, edge_cost) in graph[v].iter() {
            if dist[next] > dist[v] + edge_cost {
                dist[next] = dist[v] + edge_cost;
                heap.push((-dist[next], next));
            }
        }
    }
    let mut combination = vec![ModInt(0); n];
    combination[s] = ModInt(1);
    heap.push((-dist[s], s));
    while let Some((_, v)) = heap.pop() {
        for &(next, edge_cost) in graph[v].iter() {
            if dist[next] == dist[v] + edge_cost {
                if combination[next].0 == 0 {
                    heap.push((-dist[next], next));
                }
                let cv = combination[v];
                combination[next] += cv;
            }
        }
    }
    (dist, combination)
}

pub mod mod_int {
    use super::MOD;
    use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Sub, SubAssign};

    type Num = usize;

    #[derive(Clone, Copy)]
    pub struct ModInt<T: Copy + Clone>(pub T);

    impl Add<ModInt<Num>> for ModInt<Num> {
        type Output = ModInt<Num>;
        fn add(self, rhs: ModInt<Num>) -> ModInt<Num> {
            self + rhs.0
        }
    }

    impl Add<Num> for ModInt<Num> {
        type Output = ModInt<Num>;
        fn add(self, mut rhs: Num) -> ModInt<Num> {
            if rhs >= MOD {
                rhs %= MOD;
            }
            let mut t = rhs + self.0;
            if t >= MOD {
                t = t - MOD;
            }
            ModInt(t)
        }
    }

    impl Sub<Num> for ModInt<Num> {
        type Output = ModInt<Num>;
        fn sub(self, rhs: Num) -> ModInt<Num> {
            let rhs = if rhs >= MOD { rhs % MOD } else { rhs };
            let value = if self.0 < rhs { self.0 + MOD } else { self.0 };
            ModInt(value - rhs)
        }
    }

    impl Sub<ModInt<Num>> for ModInt<Num> {
        type Output = ModInt<Num>;
        fn sub(self, rhs: ModInt<Num>) -> ModInt<Num> {
            self - rhs.0
        }
    }

    impl AddAssign<Num> for ModInt<Num> {
        fn add_assign(&mut self, other: Num) {
            *self = *self + other;
        }
    }
    impl AddAssign<ModInt<Num>> for ModInt<Num> {
        fn add_assign(&mut self, other: ModInt<Num>) {
            *self = *self + other;
        }
    }

    impl SubAssign<Num> for ModInt<Num> {
        fn sub_assign(&mut self, other: Num) {
            *self = *self - other;
        }
    }

    impl SubAssign<ModInt<Num>> for ModInt<Num> {
        fn sub_assign(&mut self, other: ModInt<Num>) {
            *self = *self - other;
        }
    }

    impl Div<Num> for ModInt<Num> {
        type Output = ModInt<Num>;
        fn div(self, mut rhs: Num) -> ModInt<Num> {
            if rhs >= MOD {
                rhs %= MOD;
            }
            self * ModInt(rhs).pow(MOD - 2)
        }
    }

    impl Div<ModInt<Num>> for ModInt<Num> {
        type Output = ModInt<Num>;
        fn div(self, rhs: ModInt<Num>) -> ModInt<Num> {
            self / rhs.0
        }
    }

    impl DivAssign<Num> for ModInt<Num> {
        fn div_assign(&mut self, rhs: Num) {
            *self = *self / rhs
        }
    }
    impl DivAssign<ModInt<Num>> for ModInt<Num> {
        fn div_assign(&mut self, rhs: ModInt<Num>) {
            *self = *self / rhs
        }
    }

    impl Mul<ModInt<Num>> for ModInt<Num> {
        type Output = ModInt<Num>;

        fn mul(self, rhs: ModInt<Num>) -> ModInt<Num> {
            self * rhs.0
        }
    }
    impl Mul<Num> for ModInt<Num> {
        type Output = ModInt<Num>;

        fn mul(self, mut rhs: Num) -> ModInt<Num> {
            if rhs >= MOD {
                rhs %= MOD;
            }
            let t = (self.0 * rhs) % MOD;
            ModInt(t)
        }
    }

    impl MulAssign<Num> for ModInt<Num> {
        fn mul_assign(&mut self, rhs: Num) {
            *self = *self * rhs;
        }
    }

    impl MulAssign<ModInt<Num>> for ModInt<Num> {
        fn mul_assign(&mut self, rhs: ModInt<Num>) {
            *self = *self * rhs;
        }
    }

    impl ModInt<Num> {
        pub fn pow(self, e: Num) -> ModInt<Num> {
            let mut result = ModInt(1);
            let mut cur = self;
            let mut e = e;
            while e > 0 {
                if e & 1 == 1 {
                    result *= cur;
                }
                e >>= 1;
                cur *= cur;
            }
            result
        }
    }
}
pub struct IO<R, W: std::io::Write>(R, std::io::BufWriter<W>);

impl<R: std::io::Read, W: std::io::Write> IO<R, W> {
    pub fn new(r: R, w: W) -> Self {
        IO(r, std::io::BufWriter::new(w))
    }
    pub fn write<S: ToString>(&mut self, s: S) {
        use std::io::Write;
        self.1.write(s.to_string().as_bytes()).unwrap();
    }
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .0
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n' || b == b'\r' || b == b'\t')
            .take_while(|&b| b != b' ' && b != b'\n' && b != b'\r' && b != b'\t')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}


Measured memory_bytes: 22780