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
input = sys.stdin.buffer.readline
import heapq

def main():
    N,M,S = map(int,input().split())
    edge = [[] for _ in range(N)]
    for _ in range(M):
        u,v,a,b = map(int,input().split())
        edge[u-1].append((v-1, a, b))
        edge[v-1].append((u-1, a, b))
    
    change = [tuple(map(int,input().split())) for _ in range(N)]
    MAX_COST = 50*50
    S = min(S, MAX_COST)
    
    q = [(0,(0,S))]
    ans = [-1]*N
    visited = set()
    heapq.heapify(q)
    
    while q:
        time, data = heapq.heappop(q)
        now, money = data
        if ans[now] == -1:
            ans[now] = time
            if -1 not in ans:
                break
        if data in visited:
            continue
        visited.add(data)
        for fol, a, b in edge[now]:
            if money >= a:
                fol_data = (fol, money-a)
                if fol_data in visited:
                    continue
                heapq.heappush(q, (time+b, fol_data))
        c, d = change[now]
        if money+c > MAX_COST:
            continue
        heapq.heappush(q, (time+d, (now, money+c)))
    
    print(*ans[1:], sep="\n")

if __name__ == "__main__":
    main()
