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,heapify
import sys
input = sys.stdin.readline

N,M,S = map(int,input().split())
UVAB = [list(map(int,input().split())) for i in range(M)]
U,V,A,B = zip(*UVAB)

'''
from itertools import combinations 
N = 14
M = N*(N-1)//2
S = 0
UVAB = [[x,y,50,10**9] for x,y in combinations(range(1,N+1),2)] 
U,V,A,B = zip(*UVAB)
'''

mc = max(A)* M
g = defaultdict(list)

for u,v,a,b in UVAB:
    for i in range(a,mc+1):
        g[(u,i)].append(((v,i-a),b))
        g[(v,i)].append(((u,i-a),b))

CD = [[0,0]] + [list(map(int,input().split())) for i in range(N)]
#CD = [[0,0]] + [[10**9,10**9] for i in range(N)]
C,D = zip(*CD)
C = [min(c,mc) for c in C]

for i in range(1,N+1):
    for c in range(mc+1-C[i]):
        g[(i,c)].append(((i,c+C[i]),D[i]))

S = min(S,mc)
dq = [(0,S,1)]

ans = [[10**15 for j in range(mc+1)] for i in range(N+1)]
while dq:
    t, w, v = heappop(dq)
    if ans[v][w] <= t:
        continue
    for i in range(w+1):
        ans[v][i] = min(t, ans[v][i])
    for (nv,nw), nt in g[(v,w)]:
        if ans[nv][nw] > t + nt:
            heappush(dq,(t+nt,nw,nv))

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



