// ---------- begin ModInt ----------
const MOD: u32 = 1_000_000_007;

#[derive(Clone, Copy)]
struct ModInt(u32);

impl std::ops::Add for ModInt {
    type Output = ModInt;
    fn add(self, rhs: ModInt) -> Self::Output {
        let mut d = self.0 + rhs.0;
        if d >= MOD {
            d -= MOD;
        }
        ModInt(d)
    }
}

impl std::ops::AddAssign for ModInt {
    fn add_assign(&mut self, rhs: ModInt) {
        *self = *self + rhs;
    }
}

impl std::ops::Sub for ModInt {
    type Output = ModInt;
    fn sub(self, rhs: ModInt) -> Self::Output {
        let mut d = self.0 + MOD - rhs.0;
        if d >= MOD {
            d -= MOD;
        }
        ModInt(d)
    }
}

impl std::ops::SubAssign for ModInt {
    fn sub_assign(&mut self, rhs: ModInt) {
        *self = *self - rhs;
    }
}

impl std::ops::Mul for ModInt {
    type Output = ModInt;
    fn mul(self, rhs: ModInt) -> Self::Output {
        ModInt((self.0 as u64 * rhs.0 as u64 % MOD as u64) as u32)
    }
}

impl std::ops::MulAssign for ModInt {
    fn mul_assign(&mut self, rhs: ModInt) {
        *self = *self * rhs;
    }
}

impl std::ops::Neg for ModInt {
    type Output = ModInt;
    fn neg(self) -> Self::Output {
        ModInt(if self.0 == 0 {0} else {MOD - self.0})
    }
}

/* 
impl std::fmt::Display for ModInt {
    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
        write!(f, "{}", self.0)
    }
}
*/

#[allow(dead_code)]
impl ModInt {
    pub fn new(n: u32) -> ModInt {
        ModInt(n % MOD)
    }
    pub fn zero() -> ModInt {
        ModInt(0)
    }
    pub fn one() -> ModInt {
        ModInt(1)
    }
    pub fn pow(self, mut n: u32) -> ModInt {
        let mut t = ModInt::one();
        let mut s = self;
        while n > 0 {
            if n & 1 == 1 {
                t *= s;
            }
            s *= s;
            n >>= 1;
        }
        t
    }
    pub fn inv(self) -> ModInt {
        self.pow(MOD - 2)
    }
    pub fn comb(n: u32, k: u32) -> ModInt {
        if k > n {
            return ModInt::zero();
        }
        let k = std::cmp::min(k, n - k);
        let mut nu = ModInt::one();
        let mut de = ModInt::one();
        for i in 0..k {
            nu *= ModInt(n - i);
            de *= ModInt(i + 1);
        }
        nu * de.inv()
    }
}

#[allow(dead_code)]
struct Precalc {
    inv: Vec<ModInt>,
    fact: Vec<ModInt>,
    ifact: Vec<ModInt>,
}

#[allow(dead_code)]
impl Precalc {
    pub fn new(n: usize) -> Precalc {
        let mut inv = vec![ModInt::one(); n + 1];
        let mut fact = vec![ModInt::one(); n + 1];
        let mut ifact = vec![ModInt::one(); n + 1];
        for i in 2..(n + 1) {
            inv[i] = -inv[MOD as usize % i] * ModInt(MOD / i as u32);
            fact[i] = fact[i - 1] * ModInt(i as u32);
            ifact[i] = ifact[i - 1] * inv[i];
        }
        Precalc {
            inv: inv,
            fact: fact,
            ifact: ifact,
        }
    }
    pub fn inv(&self, n: usize) -> ModInt {
        self.inv[n]
    }
    pub fn fact(&self, n: usize) -> ModInt {
        self.fact[n]
    }
    pub fn ifact(&self, n: usize) -> ModInt {
        self.ifact[n]
    }
    pub fn comb(&self, n: usize, k: usize) -> ModInt {
        if k > n {
            return ModInt::zero();
        }
        self.fact[n] * self.ifact[k] * self.ifact[n - k]
    }
}
// ---------- end ModInt ----------
//https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};
    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };
    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };
    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };
    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };
    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

//

fn dijkstra(src: usize, g: &Vec<Vec<(usize, i64)>>) -> (Vec<ModInt>, Vec<i64>) {
    let n = g.len();
    let mut dp = vec![std::i64::MAX; n];
    let mut way = vec![ModInt::zero(); n];
    dp[src] = 0;
    way[src] = ModInt::one();
    let mut h = std::collections::BinaryHeap::new();
    h.push((0, src));
    while let Some((d, v)) = h.pop() {
        let d = -d;
        if d > dp[v] {
            continue;
        }
        for &(u, c) in &g[v] {
            let d = d + c;
            if dp[u] > d {
                dp[u] = d;
                way[u] = way[v];
                h.push((-d, u));
            } else if dp[u] == d {
                way[u] = way[u] + way[v];
            }
        }
    }
    (way, dp)
}

fn run() {
    input! {
        n: usize,
        m: usize,
        s: usize1,
        t: usize1,
        e: [(usize1, usize1, i64); m],
    }
    let mut g = vec![vec![]; n];
    for &(a, b, d) in &e {
        g[a].push((b, d));
        g[b].push((a, d));
    }
    let (way_s, dp_s) = dijkstra(s, &g);
    let (way_t, dp_t) = dijkstra(t, &g);
    let mut ans = way_s[t] * way_t[s];
    if dp_s[t] % 2 == 0 {
        for v in 0..n {
            if dp_s[v] * 2 == dp_s[t] {
                ans -= way_s[v].pow(2) * way_t[v].pow(2);
            }
        }
    }
    for &(a, b, d) in &e {
        if dp_s[a] + d + dp_t[b] == dp_s[t] && 2 * dp_s[a] < dp_s[t] && 2 * dp_t[b] < dp_s[t] {
            ans -= way_s[a].pow(2) * way_t[b].pow(2);
        }
        if dp_t[a] + d + dp_s[b] == dp_s[t] && 2 * dp_t[a] < dp_s[t] && 2 * dp_s[b] < dp_s[t] {
            ans -= way_t[a].pow(2) * way_s[b].pow(2);
        }
    }
    println!("{}", ans.0);
}

fn main() {
    run();
}


Measured memory_bytes: 33012