Problem:
Score : 400 points

Problem Statement

Kenkoooo is planning a trip in Republic of Snuke.
In this country, there are n cities and m trains running.
The cities are numbered 1 through n, and the i-th train connects City u_i and v_i bidirectionally.
Any city can be reached from any city by changing trains.

Two currencies are used in the country: yen and snuuk.
Any train fare can be paid by both yen and snuuk.
The fare of the i-th train is a_i yen if paid in yen, and b_i snuuk if paid in snuuk.

In a city with a money exchange office, you can change 1 yen into 1 snuuk.
However, when you do a money exchange, you have to change all your yen into snuuk.
That is, if Kenkoooo does a money exchange when he has X yen, he will then have X snuuk.
Currently, there is a money exchange office in every city, but the office in City i will shut down in i years and can never be used in and after that year.

Kenkoooo is planning to depart City s with 10^{15} yen in his pocket and head for City t, and change his yen into snuuk in some city while traveling.
It is acceptable to do the exchange in City s or City t.

Kenkoooo would like to have as much snuuk as possible when he reaches City t by making the optimal choices for the route to travel and the city to do the exchange.
For each i=0,...,n-1, find the maximum amount of snuuk that Kenkoooo has when he reaches City t if he goes on a trip from City s to City t after i years.
You can assume that the trip finishes within the year.

Constraints

2 \leq n \leq 10^5

1 \leq m \leq 10^5

1 \leq s,t \leq n

s \neq t

1 \leq u_i < v_i \leq n

1 \leq a_i,b_i \leq 10^9

If i\neq j, then u_i \neq u_j or v_i \neq v_j.

Any city can be reached from any city by changing trains.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

n m s t
u_1 v_1 a_1 b_1
:
u_m v_m a_m b_m

Output

Print n lines.
In the i-th line, print the maximum amount of snuuk that Kenkoooo has when he reaches City t if he goes on a trip from City s to City t after i-1 years.

Sample Input 1

4 3 2 3
1 4 1 100
1 2 1 10
1 3 20 1

Sample Output 1

999999999999998
999999999999989
999999999999979
999999999999897

After 0 years, it is optimal to do the exchange in City 1.

After 1 years, it is optimal to do the exchange in City 2.

Note that City 1 can still be visited even after the exchange office is closed.
Also note that, if it was allowed to keep 1 yen when do the exchange in City 2 and change the remaining yen into snuuk, we could reach City 3 with 999999999999998 snuuk, but this is NOT allowed.

After 2 years, it is optimal to do the exchange in City 3.

After 3 years, it is optimal to do the exchange in City 4.
Note that the same train can be used multiple times.

Sample Input 2

8 12 3 8
2 8 685087149 857180777
6 7 298270585 209942236
2 4 346080035 234079976
2 5 131857300 22507157
4 8 30723332 173476334
2 6 480845267 448565596
1 4 181424400 548830121
4 5 57429995 195056405
7 8 160277628 479932440
1 6 475692952 203530153
3 5 336869679 160714712
2 7 389775999 199123879

Sample Output 2

999999574976994
999999574976994
999999574976994
999999574976994
999999574976994
999999574976994
999999574976994
999999574976994

Solution in Rust (1.15.1) (judge verdict: Accepted)

use std::io::{stdin, Read, StdinLock};
use std::str::FromStr;
use std::iter::FromIterator;

fn main() {
    let cin = stdin();
    let mut scan = Scanner::new(cin.lock());
    let n = scan.read::<usize>();
    let m = scan.read::<usize>();
    let s = scan.read::<usize>()-1;
    let t = scan.read::<usize>()-1;
    let mut g = vec![vec![];n];
    let mut h = vec![vec![];n];
    for _ in 0..m {
        let u = scan.read::<usize>()-1;
        let v = scan.read::<usize>()-1;
        let a = scan.read::<i64>();
        let b = scan.read::<i64>();
        g[u].push((a, v));
        g[v].push((a, u));
        h[u].push((b, v));
        h[v].push((b, u));
    }

    let dg = dijkstra(&g, s);
    let dh = dijkstra(&h, t);
    let mut v = vec![0;n];
    for i in 0..n {
        v[i] = dg[i] + dh[i];
    }
    let segtree = SegTree::new(v, 1i64 << 60, std::cmp::min);
    for i in 0..n {
        let p = segtree.get(i..n);
        println!("{}", 1_000_000_000_000_000 - p);
    }
}

#[allow(dead_code)]
fn dijkstra(graph: &[Vec<(i64, usize)>], s: usize) -> Vec<i64> {
    let n = graph.len();
    let mut d = vec![1i64 << 60; n];
    d[s] = 0;
    let mut heap = std::collections::BinaryHeap::new();
    heap.push(Rev((0, s)));
    while let Some(Rev((p_cost, p))) = heap.pop() {
        if d[p] < p_cost {
            continue;
        }
        for &(v_cost, v) in &graph[p] {
            if d[v] > d[p] + v_cost {
                d[v] = d[p] + v_cost;
                heap.push(Rev((d[v], v)));
            }
        }
    }
    d
}

#[derive(Eq, PartialEq, Clone, Debug)]
pub struct Rev<T>(pub T);

impl<T: PartialOrd> PartialOrd for Rev<T> {
    fn partial_cmp(&self, other: &Rev<T>) -> Option<std::cmp::Ordering> {
        other.0.partial_cmp(&self.0)
    }
}

impl<T: Ord> Ord for Rev<T> {
    fn cmp(&self, other: &Rev<T>) -> std::cmp::Ordering {
        other.0.cmp(&self.0)
    }
}

use std::ops::Range;

#[allow(dead_code)]
fn contains(p: &Range<usize>, q: &Range<usize>) -> bool {
    p.start <= q.start && q.end <= p.end
}

#[allow(dead_code)]
fn separates(p: &Range<usize>, q: &Range<usize>) -> bool {
    p.end <= q.start || q.end <= p.start
}

#[allow(dead_code)]
fn size(p: &Range<usize>) -> usize {
    p.end - p.start
}

#[allow(dead_code)]
struct SegTree<'a> {
    node: Vec<i64>,
    zero: i64,
    op: Box<Fn(i64, i64) -> i64 + 'a>,
    n: usize,
}

#[allow(dead_code)]
impl <'a> SegTree<'a> {
    fn new<B>(v: Vec<i64>, zero: i64, op: B) -> SegTree<'a> where B: Fn(i64, i64) -> i64 + 'a {
        let size = v.len();
        let mut n = 1usize;
        while n < size {n *= 2}
        let mut node = vec![zero; 2*n-1];
        for i in 0..size {node[i+n-1] = v[i]}
        for i in (0..n - 1).rev() {node[i] = op(node[2*i+1], node[2*i+2])}
        SegTree {node: node, zero: zero, op: Box::new(op), n: n}
    }

    fn set(&mut self, mut x: usize, value: i64) {
        x += self.n - 1;
        self.node[x] = value;
        while x > 0 {
            x = (x - 1) / 2;
            self.node[x] = (self.op)(self.node[2*x+1], self.node[2*x+2]);
        }
    }

    fn get1(&self, i: usize) -> i64 {self.getrec(i..i+1, 0, 0..self.n)}
    fn get(&self, query: Range<usize>) -> i64 {self.getrec(query, 0, 0..self.n)}

    fn getrec(&self, query: Range<usize>, k: usize, range: Range<usize>) -> i64 {
        if separates(&query, &range) {return self.zero}
        if contains(&query, &range) {return self.node[k]}
        let vl = self.getrec(query.clone(), 2*k+1, range.start..(range.start + range.end)/2);
        let vr = self.getrec(query.clone(), 2*k+2, (range.start + range.end)/2..range.end);
        (self.op)(vl, vr)
    }
}


// region template
#[allow(dead_code)]
fn iu(i: i64) -> usize { i as usize }

#[allow(dead_code)]
fn ui(i: usize) -> i64 { i as i64 }

#[allow(dead_code, deprecated)]
fn join<T: std::fmt::Display>(slice: &[T], sep: &str) -> String {
    let strings = slice.iter().map(|t| format!("{}", t)).collect::<Vec<_>>();
    strings.connect(sep)
}

#[allow(dead_code)]
fn arr<'a, S, T>(n: usize, mut f: S) -> Vec<T> where S: FnMut(usize) -> T + 'a {
    (0..n).map(|i| f(i)).collect::<Vec<T>>()
}

#[allow(dead_code)]
fn alt<S, T>(v: Vec<S>) -> T where T: FromIterator<S> {
    v.into_iter().collect::<T>()
}

#[allow(dead_code)]
fn dup<S, T>(v: &[S]) -> T where T: FromIterator<S>, S: Clone {
    v.iter().cloned().collect::<T>()
}

struct Scanner<'a> {
    cin: StdinLock<'a>,
}

#[allow(dead_code)]
impl<'a> Scanner<'a> {
    fn new(cin: StdinLock<'a>) -> Scanner<'a> {
        Scanner { cin: cin }
    }

    fn read1<T: FromStr>(&mut self) -> Option<T> {
        let token = self.cin.by_ref().bytes().map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect::<String>();
        token.parse::<T>().ok()
    }

    fn read<T: FromStr>(&mut self) -> T {
        self.read1().unwrap()
    }

    fn readn<T: FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read::<T>()).collect()
    }

    fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}
// endregion