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 collections import defaultdict
from heapq import heappop, heappush
import sys
input = sys.stdin.readline


N, M, S = map(int, input().split())

d = defaultdict(list)
e = defaultdict(int)

for _ in range(M):
    U, V, A, B = map(int, input().split())
    d[U].append((A, B, V))
    d[V].append((A, B, U))

for i in range(1, N+1):
    C, D = map(int, input().split())
    e[i] = (C, D)

dist = defaultdict(lambda :10**30)
ans = defaultdict(lambda :10**30)

source = (1, S)
dist[source] = 0
q = [(0, source)]

while q:
    cost, (s, nokori) = heappop(q)
    ns = (s, nokori)

    u, v = e[s]
    if dist[ns] < cost:
        continue

    if nokori > 2500:
        nokori = 2500
    else:
        n_nokori = nokori + u
        n_cost = v
        if n_nokori > 2500:
            n_nokori = 2500
        nt = (s, n_nokori)
        
        if dist[nt] > dist[ns]+n_cost:
            dist[nt] = dist[ns]+n_cost
            heappush(q, (dist[nt], nt))
    
    for a, b, t in d[s]:
        n_nokori = nokori - a
        n_cost = b
        
        nt = (t, n_nokori)

        if n_nokori < 0:
            continue
        if dist[nt] > dist[ns]+n_cost:
            dist[nt] = dist[ns]+n_cost
            heappush(q, (dist[nt], nt))

for (s, _), v in dist.items():
    ans[s] = min(ans[s], v)

for i in range(2, N+1):
    print(ans[i])