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)

#![allow(unused_imports)]
#![allow(dead_code)]
#![allow(unused_must_use)]
use std::io::{stdin, stdout, stderr, Write, BufWriter, BufReader, BufRead};
use std::collections::BinaryHeap;

use util::IterExt;
macro_rules! read_from_line {
    ($inbuf:ident => $($name:ident : $ty:ty),* ) => {
        let mut buf = String::new();
        $inbuf.read_line(&mut buf).unwrap();
        buf.pop();
        let mut words = buf.split_whitespace();
        $(
            let $name:$ty = words.next().unwrap().parse().unwrap();
        )*
    };
}

macro_rules! read_many {
    ($inbuf:ident => $name:ident : $ty:ty) => {
        let $name: Vec<$ty> = strio::read_many_from_line(&mut $inbuf);
    };
}

#[derive(PartialEq, Eq, Debug)]
struct RevOrd<T>(T);

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

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

#[derive(Debug)]
struct KV<K, V> {
    k: K,
    v: V
}
impl <K, V> KV<K, V> {
    fn new(k: K, v: V) -> Self {
        KV {k:k, v:v}
    }
}
impl <K, V> PartialEq for KV<K, V> where V: PartialEq {
    fn eq(&self, other: &Self) -> bool {
        self.v.eq(&other.v)
    }
}
impl <K, V> Eq for KV<K, V> where V: Eq { }
impl<K, V> PartialOrd for KV<K, V> where V: PartialOrd {
    fn partial_cmp(&self, other: &Self) -> Option<std::cmp::Ordering> {
        self.v.partial_cmp(&other.v)
    }
}
impl<K, V> Ord for KV<K, V> where V: Ord {
    fn cmp(&self, other: &Self) -> std::cmp::Ordering {
        self.v.cmp(&other.v)
    }
}


fn main() {
    let cout = stdout();
    let mut cout = BufWriter::new(cout.lock());
    let cin = stdin();
    let mut cin = BufReader::new(cin.lock());

    #[derive(Clone, Copy)]
    struct Edge {
        to: usize,
        yen: usize,
        snuke: usize,
    }

    read_from_line!(cin => n:usize, m:usize, s:usize, t:usize);
    let mut edge : Vec<Vec<Edge>> = vec![vec![]; n + 1];
    for i in 1 .. m + 1 {
        read_from_line!(cin => u:usize, v:usize, yen:usize, snuke:usize);
        edge[u].push(Edge{to:v, yen:yen, snuke:snuke});
        edge[v].push(Edge{to:u, yen:yen, snuke:snuke});
    }

    fn dijkstra_all<F>(es: &Vec<Vec<Edge>>, x: usize, sel: F) -> Vec<Option<usize>> where
        F: Fn(&Edge) -> usize
    {
        let mut ans = vec![None; es.len()];
        let mut q = BinaryHeap::new();
        q.push(RevOrd(KV::new(x, 0)));
        while let Some(p) = q.pop() {
            let vtx = p.0.k;
            let cost = p.0.v;
            if ans[vtx].map(|x| x <= cost) == Some(true) {
                continue;
            }

            ans[vtx] = Some(cost);
            for e in es[vtx].iter() {
                let edge_cost = sel(e);
                q.push(RevOrd(KV::new(e.to, cost + edge_cost)))
            }
        }
        ans
    }
    let yen_map = dijkstra_all(&edge, s, |e| e.yen);
    let snuke_map = dijkstra_all(&edge, t, |e| e.snuke);

    let min_with_exchange = (0..n+1)
        .map(|n| {
            match (yen_map[n], snuke_map[n]) {
                (Some (x), Some(y)) => Some (x + y),
                _ => None
            }
        }).collect::<Vec<Option<usize>>>();
    let mut min_cost = vec![None; n + 1];
    let mut min = None::<usize>;
    for i in (1..n+1).rev() {
        min = match min {
            None => min_with_exchange[i],
            Some(c) => match min_with_exchange[i] {
                None => Some(c),
                Some(d) => Some(std::cmp::min(c, d))
            },
        };
        min_cost[i] = min;
    }

    for i in 1..n+1 {
        writeln!(cout, "{}", 1000000000000000 - min_cost[i].unwrap()).unwrap();
    }

    
    /*
    let accum: Vec<i64> = xs.iter().accum(0).collect();
    println!("{:?}", accum);
    */
}


mod util {
    use std;
    use std::ops::{Deref, AddAssign};
    use std::iter::{Once, Chain, Scan};
    use std::borrow::Borrow;

    pub trait IterExt where
        Self: Iterator
    {
        fn scan_init<'a, St : 'a, F : 'a> (self, initial_state: St, f: F) -> Box<Iterator<Item=St> + 'a> /*Chain<Once<St>, Scan<Self, St, F>>*/  where
            Self: Sized + 'a,
            F: FnMut(&mut St, Self::Item) -> Option<St>,
            St: Clone
        {
            Box::new(std::iter::once(initial_state.clone()).chain(self.scan(initial_state, f)))
        }

        fn accum<'a, T> (self, init: T) -> Box<Iterator<Item=T> + 'a> where
            Self: Sized + 'a,
            Self::Item: Borrow<T>,
            T: Clone + AddAssign + 'a,
        {
            Box::new(self.scan_init(init, |sum, x| { *sum += x.borrow().clone(); Some(sum.clone()) }))
        }
    }

    impl<T> IterExt for T where
        T: Iterator
    { }

    pub fn test()
    {
        let v:Vec<i32> = vec![1, 4 ,2];
        for x in v.iter().accum(0) {
            println!("{}", x);
        }
        for x in v.iter().accum(0).accum(0) {
            println!("{}", x);
        }

    }

}

mod strio {
    use std::str::FromStr;
    use std;

    pub fn read_from_line<T, R> (r: &mut R) -> T where
        T: FromStr,
        <T as std::str::FromStr>::Err : std::fmt::Debug,
        R: std::io::BufRead,
    {
        let mut buf = String::new();
        r.read_line(&mut buf).unwrap();
        buf.pop();
        buf.parse().unwrap()
    }

    pub fn read_many_from_line<T, R> (r: &mut R) -> Vec<T> where
        T: FromStr,
        <T as std::str::FromStr>::Err : std::fmt::Debug,
        R: std::io::BufRead,
    {
        let mut buf = String::new();
        r.read_line(&mut buf).unwrap();
        buf.pop();
        buf.split_whitespace().map(|x| x.parse().unwrap()).collect()
    }
}