There are N cities numbered 1 to N, connected by M railroads.

You are now at City 1, with 10^{100} gold coins and S silver coins in your pocket.

The i-th railroad connects City U_i and City V_i bidirectionally, and a one-way trip costs A_i silver coins and takes B_i minutes. You cannot use gold coins to pay the fare.

There is an exchange counter in each city. At the exchange counter in City i, you can get C_i silver coins for 1 gold coin. The transaction takes D_i minutes for each gold coin you give. You can exchange any number of gold coins at each exchange counter.

For each t=2, ..., N, find the minimum time needed to travel from City 1 to City t. You can ignore the time spent waiting for trains.

Constraints

* 2 \leq N \leq 50
* N-1 \leq M \leq 100
* 0 \leq S \leq 10^9
* 1 \leq A_i \leq 50
* 1 \leq B_i,C_i,D_i \leq 10^9
* 1 \leq U_i < V_i \leq N
* There is no pair i, j(i \neq j) such that (U_i,V_i)=(U_j,V_j).
* Each city t=2,...,N can be reached from City 1 with some number of railroads.
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N M S
U_1 V_1 A_1 B_1
:
U_M V_M A_M B_M
C_1 D_1
:
C_N D_N


Output

For each t=2, ..., N in this order, print a line containing the minimum time needed to travel from City 1 to City t.

Examples

Input

3 2 1
1 2 1 2
1 3 2 4
1 11
1 2
2 5


Output

2
14


Input

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


Output

5
5
7


Input

6 5 1
1 2 1 1
1 3 2 1
2 4 5 1
3 5 11 1
1 6 50 1
1 10000
1 3000
1 700
1 100
1 1
100 1


Output

1
9003
14606
16510
16576


Input

4 6 1000000000
1 2 50 1
1 3 50 5
1 4 50 7
2 3 50 2
2 4 50 4
3 4 50 3
10 2
4 4
5 5
7 7


Output

1
3
5


Input

2 1 0
1 2 1 1
1 1000000000
1 1


Output

1000000001
import sys
from heapq import *
input = sys.stdin.readline


def main():
    n, m, s = map(int, input().split())
    
    s = min(s, 2500)
    
    railway = [[] for _ in range(n)]
    for i in range(m):
        u, v, a, b = map(int, input().split())
        railway[u-1].append((v-1, a, b))
        railway[v-1].append((u-1, a, b))
    
    exchange = [None]*n
    for i in range(n):
        exchange[i] = tuple(map(int, input().split()))
    
    
    judge = [(0, 0, s)]
    heapify(judge)
    time = [[-1]*2501 for _ in range(n+1)]*n
    
    while judge:
        t, now, money = heappop(judge)
        if time[now][money] == -1:
            time[now][money] = t
        elif time[now][money] <= t:
            continue
        else:
            time[now][money] = min(time[now][money], t)
        
        if money < 2500:
            c, d = exchange[now]
            if time[now][min(2500, money+c)] == -1:
                heappush(judge, (t+d, now, min(2500, money+c)))
        for (v, a, b) in railway[now]:
            if money-a < 0:
                continue
            if time[v][money-a] == -1:
                heappush(judge, (t+b, v, money-a))
    
    for i in range(1, n):
        print(min(time[i]))
    
    
if __name__ == "__main__":
    main()
