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 Python3 (judge verdict: Wrong Answer)

import sys
import heapq


def dfs(u,s,target, route=None):
    if(route == None):
        route=[]
    route.append(u)
    global h
    if(u == target):
        heapq.heappush(h,s)
        return
    for j in range(e):
        if(e_1[j] == u):
            if e_2[j] not in route[0:len(route)-1]:
                
                s = s + e_w[j]
                dfs(e_2[j],s,target,route[0:])


v,e,r=map(int, input().split());

vs=[0]*v;

e_1=[0]*e;
e_2=[0]*e;
e_w=[0]*e;

for i in range(v):
    vs[i] = 0;
for i in range(e):
    e_1[i], e_2[i], e_w[i] = map(int, input().split());

for i in range(v):
    h = []
    dfs(r,0,i)
    if(len(h) != 0):
        print(heapq.heappop(h))
    else:
        print("INF")