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 heappop, heappush

n, m, ss = map(int, input().split())
lines = sys.stdin.readlines()
links = [set() for _ in range(n)]
aaa = []
for line in lines[:m]:
    u, v, a, b = map(int, line.split())
    u -= 1
    v -= 1
    links[u].add((v, a, b))
    links[v].add((u, a, b))
    aaa.append(a)

exchanges = []
for line in lines[m:]:
    c, d = map(int, line.split())
    exchanges.append((c, d))

req = sum(sorted(aaa, reverse=True)[:n - 1])
INF = 10 ** 18
ans = [INF] * n
ans_silver = [-1] * n

q = [(0, ss, 0)]  # (time, silver, city)
visited = set()
fixed = 0
while q:
    t, s, v = heappop(q)
    if (s, v) in visited or ans_silver[v] >= s:
        continue
    visited.add((s, v))
    if ans[v] == INF:
        ans[v] = t
        ans_silver[v] = s
        fixed += 1
        if fixed == n:
            break

    for u, a, b in links[v]:
        if s < a:
            continue
        ns = s - a
        nt = t + b
        if (ns, u) in visited or ans_silver[u] >= ns:
            continue
        heappush(q, (nt, ns, u))

    c, d = exchanges[v]
    ns = s + c
    if ns <= req and (ns, v) not in visited:
        heappush(q, (t + d, ns, v))

print('\n'.join(map(str, ans[1:])))
