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
[print(min(m[i])[0])for h in[__import__('heapq')]for a,d,r,n,x in[(h.heappush,h.heappop,range,lambda:map(int,input().split()),list.append)]for N,M,S in[n()]for g,q in[([[]for _ in r(N)],[(0,S,0)])]for L in[max(A for _ in r(M)for U,V,A,B in[n()]if not(x(g[U-1],(V-1,A,B))or x(g[V-1],(U-1,A,B))))*(N-1)]for m in[[[[2**64]for _ in r(L+1)]for _ in r(N)]]for _ in[[[x(g[i],(i,-C,D))for i in r(N)for C,D in[n()]],[[[_ for s,v,i in[d(q)]for _ in[[a(q,(s+c,j,t))for t,p,c in g[i]for j in[min(L,v-p)]for y in[m[t][j]]if v>=p and s+c<y[0] and not(y.clear()or x(y,s+c))]]if not(x(l,None)if q else l.clear())]]for l in[[None]]for _ in l]]]for i in r(1,N)]
