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
def input(): return sys.stdin.readline().strip()
def mapint(): return map(int, input().split())
sys.setrecursionlimit(10**9)

N, M, S = mapint()
graph = [{} for _ in range(N)]
for _ in range(M):
    u, v, a, t = mapint()
    graph[u-1][v-1] = (a, t)
    graph[v-1][u-1] = (a, t)

change = [list(mapint()) for _ in range(N)]
from heapq import heappop, heappush
# time, silver, vertex
Q = [(0, min(2500, S), 0)]
dist = [[10**18]*2501 for _ in range(N)]
dist[0][min(2500, S)] = 0

while Q:
    t, s, v = heappop(Q)
    rate, change_time = change[v]
    if s<2500 and dist[v][min(2500, s+rate)]>t+change_time:
        dist[v][min(2500, s+rate)] = t+change_time
        heappush(Q, (t+change_time, min(2500, s+rate), v))
    for nx in graph[v].keys():
        nx_s, nx_t = graph[v][nx]
        if nx_s<=s and dist[nx][s-nx_s]>t+nx_t:
            dist[nx][s-nx_s] = t+nx_t
            heappush(Q, (t+nx_t, s-nx_s, nx))
for i in range(1, N):
    print(min(dist[i]))