Problem:
Single Source Shortest Path

For a given weighted graph G(V, E) and a source r, find the source shortest path to each vertex from the source (SSSP: Single Source Shortest Path).

Input

An edge-weighted graph G (V, E) and the source r.

|V| |E| r
s0 t0 d0
s1 t1 d1
:
s|E|-1 t|E|-1 d|E|-1

|V| is the number of vertices and |E| is the number of edges in G. The graph vertices are named with the numbers 0, 1,..., |V|-1 respectively. r is the source of the graph.

si and ti represent source and target vertices of i-th edge (directed) and di represents the cost of the i-th edge.

Output

Print the costs of SSSP in the following format.

c0
c1
:
c|V|-1

The output consists of |V| lines. Print the cost of the shortest path from the source r to each vertex 0, 1, ... |V|-1 in order. If there is no path from the source to a vertex, print INF.

Constraints

1 ≤ |V| ≤ 100000

0 ≤ di ≤ 10000

0 ≤ |E| ≤ 500000

There are no parallel edges

There are no self-loops

Sample Input 1

4 5 0
0 1 1
0 2 4
1 2 2
2 3 1
1 3 5

Sample Output 1

0
1
3
4

Sample Input 2

4 6 1
0 1 1
0 2 4
2 0 1
1 2 2
3 1 1
3 2 5

Sample Output 2

3
0
2
INF

Solution in Rust (judge verdict: Wrong Answer)

#[allow(unused_imports)]
use std::cmp::{min,max};
use std::collections::BinaryHeap;

fn main() {
    let xs = read_vec_i64();
    let (v,e,r) = (xs[0] as usize, xs[1] as usize, xs[2] as usize);
    let mut adj = vec![];
    adj.resize(v,vec![]);
    for _ in 0..e {
        let ys = read_vec_i64();
        let (s,t,d) = (ys[0] as usize, ys[1] as usize, ys[2]);
        adj[s].push((t,d));
    }
    let inf = 1 << 29;
    let mut dists = vec![];
    dists.resize(v, inf);
    dists[r] = 0;
    let mut heap = BinaryHeap::new();
    heap.push((0,r));
    while let Some((md,s)) = heap.pop() {
        let d = -md;
        for t_dd in adj[s].iter() {
            let (t,dd) = *t_dd;
            let nd = d + dd;
            if nd < dists[t] {
                dists[t] = nd;
                heap.push((-nd,t));
            }
        }
    }
    for d in dists {
        if d != inf {
            println!("{}", d);
        }
        else {
            println!("INF");
        }
    }
}

#[allow(dead_code)]
fn read_line() -> String {
    let mut ret = String::new();
    std::io::stdin().read_line(&mut ret).ok();
    ret.pop();
    return ret;
}

#[allow(dead_code)]
fn read_i64() -> i64 {
    let ss = read_line();
    let mut ret :i64 = 0;
    for c in ss.chars() {
        if ! ('0' <= c && c <= '9') { break; }
        let t = c.to_digit(10).unwrap() as i64;
        ret = ret * 10 + t;
    }
    return ret;
}

#[allow(dead_code)]
fn read_vec_i64() -> Vec<i64> {
    let ss = read_line();
    let mut res = Vec::new();
    let mut edited = false;
    let mut x:i64 = 0;
    for c in ss.chars() {
        if !('0' <= c && c <= '9') {
            if edited {
                edited = false;
                res.push(x);
                x = 0;
            }
        }
        else {
            let t = c.to_digit(10).unwrap() as i64;
            x = x * 10 + t;
            edited = true;
        }
    }
    if edited {
        res.push(x);
    }
    return res;
}