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
from heapq import heappop, heappush
import sys
def main():
    input = sys.stdin.readline
    N, M, S = map(int, input().split())
    G1 = [[] for _ in range(N)]
    for _ in range(M):
        u, v, a, b = map(int, input().split())
        u, v = u - 1, v - 1
        G1[u].append((b, a, v))
        G1[v].append((b, a, u))
    G2 = [tuple(map(int, input().split())) for _ in range(N)]

    q = [(0, (0, S))]
    T = [-1] * N
    lenT = 0
    visited = set()
    MX = 50 * (N - 1)
    while q:
        t, V = heappop(q)
        v, s = V
        if T[v] < 0:
            T[v] = t
            lenT += 1
            if lenT >= N: break
        if V in visited: continue
        visited.add(V)
        for dt, ds, to in G1[v]:
            if s < ds: continue
            nV = (to, s - ds)
            if nV in visited: continue
            heappush(q, (t + dt, nV))
        c, d = G2[v]
        if s + c <= MX:
            heappush(q, (t + d, (v, s + c)))
    for i in range(1, N):
        print(T[i])

if __name__ == '__main__':
    main()
