use proconio::{input, marker::Usize1};
use std::cmp::Reverse;

// modint {{{
mod modint {
    pub trait ModValue:
        std::ops::Add<Output = Self>
        + std::ops::Sub<Output = Self>
        + std::ops::Mul<Output = Self>
        + std::ops::Div<Output = Self>
        + std::ops::Rem<Output = Self>
        + std::ops::AddAssign
        + std::ops::SubAssign
        + std::ops::MulAssign
        + std::ops::DivAssign
        + std::ops::RemAssign
        + std::ops::Neg
        + std::cmp::Ord
        + Clone
        + Copy
        + Sized
        + std::fmt::Debug
        + std::fmt::Display
    {
    }

    impl<
            Value: std::ops::Add<Output = Self>
                + std::ops::Sub<Output = Self>
                + std::ops::Mul<Output = Self>
                + std::ops::Div<Output = Self>
                + std::ops::Rem<Output = Self>
                + std::ops::AddAssign
                + std::ops::SubAssign
                + std::ops::MulAssign
                + std::ops::DivAssign
                + std::ops::RemAssign
                + std::ops::Neg
                + std::cmp::Ord
                + Clone
                + Copy
                + Sized
                + std::fmt::Debug
                + std::fmt::Display,
        > ModValue for Value
    {
    }

    pub trait Minfo: Clone + Copy + std::fmt::Debug {
        type Value: ModValue;

        fn modulus() -> Self::Value;

        fn zero() -> Self::Value;

        fn one() -> Self::Value;
    }

    #[derive(Clone, Copy, Debug)]
    pub struct Mint<Mod: Minfo>(Mod::Value);

    impl<Mod: Minfo> Mint<Mod> {
        #[inline]
        #[allow(dead_code)]
        fn is_within_the_range(x: Mod::Value) -> bool {
            Mod::zero() <= x && x < Mod::modulus()
        }

        #[inline]
        #[allow(dead_code)]
        fn normalize(x: Mod::Value) -> Mod::Value {
            if Self::is_within_the_range(x) {
                x
            } else {
                let x = x % Mod::modulus();
                if x < Mod::zero() {
                    x + Mod::modulus()
                } else {
                    x
                }
            }
        }

        #[allow(dead_code)]
        pub fn zero() -> Self {
            Self(Mod::zero())
        }

        #[allow(dead_code)]
        pub fn one() -> Self {
            Self(Mod::one())
        }

        #[allow(dead_code)]
        pub fn modulus() -> Mod::Value {
            Mod::modulus()
        }

        #[allow(dead_code)]
        pub fn is_zero(&self) -> bool {
            self.value() == Mod::zero()
        }

        #[allow(dead_code)]
        pub fn from_value(x: Mod::Value) -> Self {
            Self(Self::normalize(x))
        }

        #[allow(dead_code)]
        pub fn value(&self) -> Mod::Value {
            self.0
        }

        #[allow(dead_code)]
        pub fn inv(&self) -> Self {
            if self.is_zero() {
                panic!("inv(0)");
            }
            Self(Self::raw_inv(self.value()))
        }

        #[allow(dead_code)]
        pub fn pow(&self, b: u64) -> Self {
            Self(Self::raw_pow(self.value(), b))
        }

        fn raw_add(x: Mod::Value, y: Mod::Value) -> Mod::Value {
            let z = x + y;
            if Mod::modulus() <= z {
                z - Mod::modulus()
            } else {
                z
            }
        }

        fn raw_sub(x: Mod::Value, y: Mod::Value) -> Mod::Value {
            let z = x - y;
            if z < Mod::zero() {
                z + Mod::modulus()
            } else {
                z
            }
        }

        fn raw_neg(x: Mod::Value) -> Mod::Value {
            if x == Mod::zero() {
                Mod::zero()
            } else {
                Mod::modulus() - x
            }
        }

        fn raw_mul(x: Mod::Value, y: Mod::Value) -> Mod::Value {
            x * y % Mod::modulus()
        }

        fn raw_div(x: Mod::Value, y: Mod::Value) -> Mod::Value {
            Self::raw_mul(x, Self::raw_inv(y))
        }

        #[allow(clippy::many_single_char_names)]
        fn raw_inv(mut x: Mod::Value) -> Mod::Value {
            let mut y = Mod::modulus();
            let mut u = Mod::one();
            let mut v = Mod::zero();
            while x != Mod::zero() {
                let q = y / x;
                y -= x * q;
                v -= u * q;
                std::mem::swap(&mut x, &mut y);
                std::mem::swap(&mut u, &mut v);
            }
            Self::normalize(v)
        }

        fn raw_pow(mut a: Mod::Value, mut b: u64) -> Mod::Value {
            let mut x = Mod::one();
            while 0 < b {
                if b % 2 == 1 {
                    x = Self::raw_mul(x, a);
                }
                a = Self::raw_mul(a, a);
                b /= 2
            }
            x
        }
    }

    macro_rules! impl_biop {
        (
            $(
                $biop_trait: ident::$biop_fn: ident,
                $biop_assign_trait: ident::$biop_assign_fn: ident,
                $biop_impl: ident;
            )*
        ) => {
            $(
                impl<Mod: Minfo> std::ops::$biop_trait for Mint<Mod> {
                    type Output = Self;
                    fn $biop_fn(self, rhs: Self) -> Self::Output {
                        Mint(Self::$biop_impl(self.value(), rhs.value()))
                    }
                }
                impl<Mod: Minfo> std::ops::$biop_assign_trait for Mint<Mod>
                where
                    Self: Copy
                {
                    fn $biop_assign_fn(&mut self, rhs: Self) {
                        use std::ops::$biop_trait;
                        *self = Mint::$biop_fn(*self, rhs)
                    }
                }
            )*
        };
    }

    impl_biop! {
        Add::add, AddAssign::add_assign, raw_add;
        Sub::sub, SubAssign::sub_assign, raw_sub;
        Mul::mul, MulAssign::mul_assign, raw_mul;
        Div::div, DivAssign::div_assign, raw_div;
    }

    impl<Mod: Minfo> std::ops::Neg for Mint<Mod> {
        type Output = Self;
        fn neg(self) -> Self::Output {
            Self(Self::raw_neg(self.value()))
        }
    }

    impl<Mod: Minfo> std::cmp::PartialEq for Mint<Mod> {
        fn eq(&self, other: &Self) -> bool {
            self.value().eq(&other.value())
        }
    }
    impl<Mod: Minfo> std::cmp::Eq for Mint<Mod> {}

    impl<Mod: Minfo> std::fmt::Display for Mint<Mod> {
        fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
            write!(f, "{}", self.value())
        }
    }

    impl<Mod: Minfo> std::iter::Sum<Self> for Mint<Mod> {
        fn sum<I: Iterator<Item = Self>>(iter: I) -> Self {
            iter.fold(Mint::zero(), |acc, x| acc + x)
        }
    }

    impl<Mod: Minfo> std::iter::Product<Self> for Mint<Mod> {
        fn product<I: Iterator<Item = Self>>(iter: I) -> Self {
            iter.fold(Mint::one(), |acc, x| acc * x)
        }
    }

    #[allow(dead_code)]
    pub struct Factorial<Mod: Minfo> {
        normal: Vec<Mint<Mod>>,
        inverted: Vec<Mint<Mod>>,
    }

    #[allow(dead_code)]
    impl<Mod: Minfo> Factorial<Mod>
    where
        Mod::Value: std::convert::TryFrom<usize, Error = std::num::TryFromIntError>,
    {
        pub fn new(n: usize) -> Self {
            if n == 0 {
                Self {
                    normal: Vec::new(),
                    inverted: Vec::new(),
                }
            } else {
                use std::convert::TryFrom;
                let mut normal = vec![Mint::one(); n];
                for i in 1..n {
                    normal[i] = normal[i - 1] * Mint::from_value(Mod::Value::try_from(i).unwrap());
                }
                let mut inverted = vec![Mint::one(); n];
                inverted[n - 1] = normal[n - 1].inv();
                for i in (1..n).rev() {
                    inverted[i - 1] =
                        inverted[i] * Mint::from_value(Mod::Value::try_from(i).unwrap());
                }
                Self { normal, inverted }
            }
        }
    }

    #[allow(dead_code)]
    impl<Mod: Minfo> Factorial<Mod> {
        pub fn is_empty(&self) -> bool {
            self.normal.is_empty()
        }

        pub fn len(&self) -> usize {
            self.normal.len()
        }

        pub fn inverted(&self, i: usize) -> Mint<Mod> {
            self.inverted[i]
        }

        pub fn falling(&self, x: usize, p: usize) -> Mint<Mod> {
            if p == 0 {
                Mint::one()
            } else if x < p {
                Mint::zero()
            } else {
                assert!(x < self.len());
                self[x] * self.inverted(x - p)
            }
        }

        pub fn binom(&self, n: usize, k: usize) -> Mint<Mod> {
            if n < k {
                Mint::zero()
            } else {
                assert!(n < self.len());
                self[n] * self.inverted(k) * self.inverted(n - k)
            }
        }
    }

    #[allow(dead_code)]
    impl<Mod: Minfo, I: std::slice::SliceIndex<[Mint<Mod>]>> std::ops::Index<I> for Factorial<Mod> {
        type Output = I::Output;

        #[inline]
        fn index(&self, index: I) -> &Self::Output {
            &self.normal[index]
        }
    }

    #[allow(dead_code)]
    pub struct DoubleFactorial<Mod: Minfo> {
        normal: Vec<Mint<Mod>>,
        inverted: Vec<Mint<Mod>>,
    }

    #[allow(dead_code)]
    impl<Mod: Minfo> DoubleFactorial<Mod>
    where
        Mod::Value: std::convert::TryFrom<usize, Error = std::num::TryFromIntError>,
    {
        pub fn new(n: usize) -> Self {
            use std::convert::TryFrom;
            let mut normal = vec![Mint::one(); n];
            for i in 2..n {
                normal[i] = normal[i - 2] * Mint::from_value(Mod::Value::try_from(i).unwrap());
            }
            let mut inverted = vec![Mint::one(); n];
            inverted[n - 1] = normal[n - 1].inv();
            inverted[n - 2] = normal[n - 2].inv();
            for i in (2..n).rev() {
                inverted[i - 2] = inverted[i] * Mint::from_value(Mod::Value::try_from(i).unwrap());
            }
            Self { normal, inverted }
        }
    }

    #[allow(dead_code)]
    impl<Mod: Minfo> DoubleFactorial<Mod> {
        pub fn inverted(&self, i: usize) -> Mint<Mod> {
            self.inverted[i]
        }
    }

    #[allow(dead_code)]
    impl<Mod: Minfo, I: std::slice::SliceIndex<[Mint<Mod>]>> std::ops::Index<I>
        for DoubleFactorial<Mod>
    {
        type Output = I::Output;

        #[inline]
        fn index(&self, index: I) -> &Self::Output {
            &self.normal[index]
        }
    }

    #[macro_export]
    macro_rules! define_mint {
        (
            struct $modint: ident ($modinfo: ident ($modvalue: expr; $modty: ty));
        ) => {
            #[allow(dead_code)]
            #[derive(Clone, Copy, Debug)]
            pub struct $modinfo {}
            impl Minfo for $modinfo {
                type Value = $modty;
                fn modulus() -> Self::Value {
                    $modvalue
                }
                fn zero() -> Self::Value {
                    0
                }
                fn one() -> Self::Value {
                    1
                }
            }
            type $modint = Mint<$modinfo>;
        };
    }

    #[allow(dead_code)]
    #[derive(Clone, Copy, Debug)]
    pub struct Minfo1000000007 {}

    impl Minfo for Minfo1000000007 {
        type Value = i64;
        fn modulus() -> Self::Value {
            1_000_000_007
        }
        fn zero() -> Self::Value {
            0
        }
        fn one() -> Self::Value {
            1
        }
    }

    #[allow(dead_code)]
    pub type Mint1000000007 = Mint<Minfo1000000007>;

    #[allow(dead_code)]
    #[derive(Clone, Copy, Debug)]
    pub struct Minfo998244353 {}

    impl Minfo for Minfo998244353 {
        type Value = i64;
        fn modulus() -> Self::Value {
            998_244_353
        }
        fn zero() -> Self::Value {
            0
        }
        fn one() -> Self::Value {
            1
        }
    }

    #[allow(dead_code)]
    pub type Mint998244353 = Mint<Minfo998244353>;
}
// }}}

type Mint = modint::Mint1000000007;

fn main() {
    input!(
        n: usize,
        m: usize,
        s: Usize1,
        t: Usize1,
        uvd: [(Usize1, Usize1, u64); m]
    );

    let mut g = vec![vec![]; n];
    for &(u, v, d) in &uvd {
        g[u].push((v, d));
        g[v].push((u, d));
    }

    let mut heap = std::collections::BinaryHeap::from(vec![(Reverse(0), s)]);
    let mut dist = vec![std::u64::MAX; n];
    dist[s] = 0;
    while let Some((Reverse(dx), x)) = heap.pop() {
        if dist[x] < dx {
            continue;
        }
        for &(y, w) in &g[x] {
            let dy = dx + w;
            if dist[y] <= dy {
                continue;
            }
            dist[y] = dy;
            heap.push((Reverse(dy), y));
        }
    }
    let dist_s2t = dist[t];

    let mut ord: Vec<usize> = (0..n).collect();
    ord.sort_by_key(|&i| dist[i]);
    let mut on_shortest = vec![false; n];
    on_shortest[t] = true;
    let mut dp = vec![Mint::zero(); n];
    let mut ep = vec![Mint::zero(); n];
    dp[s] = Mint::one();
    ep[t] = Mint::one();
    for &x in &ord {
        for &(y, d) in &g[x] {
            if dist[x] + d == dist[y] {
                let dpx = dp[x];
                dp[y] += dpx;
            }
        }
    }
    for x in ord.iter().copied().rev() {
        for &(y, d) in &g[x] {
            if dist[x] == dist[y] + d {
                let epx = ep[x];
                ep[y] += epx;
                on_shortest[y] |= on_shortest[x];
            }
        }
    }

    println!(
        "{}",
        dp[t].pow(2)
            - dist
                .iter()
                .copied()
                .enumerate()
                .filter_map(|(i, d)| if on_shortest[i] && 2 * d == dist_s2t {
                    Some(dp[i] * ep[i])
                } else {
                    None
                })
                .chain(uvd.iter().filter_map(|&(u, v, w)| {
                    let du = dist[u];
                    let dv = dist[v];
                    if on_shortest[u] && on_shortest[v] && du.max(dv) - du.min(dv) == w {
                        if 2 * du < dist_s2t && dist_s2t < 2 * dv {
                            Some(dp[u] * ep[v])
                        } else if 2 * dv < dist_s2t && dist_s2t < 2 * du {
                            Some(dp[v] * ep[u])
                        } else {
                            None
                        }
                    } else {
                        None
                    }
                }))
                .map(|x| x * x)
                .sum::<Mint>()
    );
}


Measured memory_bytes: 26944