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 heapq as hq
n,m,s = list(map(int,input().split()))
G = [[] for _ in range(n)]

for i in range(m):
  u,v,A,B = list(map(int,input().split()))
  u -= 1
  v -= 1
  hq.heappush(G[u], (B,A,v))
  hq.heappush(G[v], (B,A,u))
  #G[u].append((B,A,v))
  #G[v].append((B,A,u))

c = [0]*n
d = [0]*n
for i in range(n):
  C,D = list(map(int,input().split()))
  c[i] = C
  d[i] = D

inf = 1<<61
M = 50*51
if s > M:s = M-1
dp = [[inf] * M for _ in range(n)] 
cur = 0
dp[cur][s] = 0
que = [(0,s,0)]
while que:
  cd,cs,cur = hq.heappop(que)
  C = c[cur];D = d[cur]
  if dp[cur][cs] < cd:continue
  if cs+C < M and cd+D < dp[cur][cs+C]:
    dp[cur][cs+C] = cd+D
    hq.heappush(que, (cd+D, cs+C, cur))
  for g in G[cur]:
    B = g[0];A = g[1];to = g[2]
    if cs >= A and B+cd < dp[to][cs-A]:
      dp[to][cs-A] = B+cd
      hq.heappush(que, (B+cd, cs-A, to))

for i in range(1,n):
  print(min(dp[i]))
