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
#include <bits/stdc++.h>
using namespace std;

struct Edge {
    int to, coin;
    int64_t cost;
    Edge(int _to, int _coin, int64_t _cost) : to(_to), coin(_coin), cost(_cost) {}
};

const int MAX = 2525;
const int64_t INF = 1e18;

int main() {
    int N, M, S;
    cin >> N >> M >> S;
    vector<vector<Edge>> G(N);
    for(int i = 0; i < M; ++i) {
        int u, v, a, b;
        cin >> u >> v >> a >> b;
        u--, v--;
        G[u].emplace_back(v, a, b);
        G[v].emplace_back(u, a, b);
    }
    vector<int> C(N), D(N);
    for(int i = 0; i < N; ++i) cin >> C[i] >> D[i];

    using V = tuple<int64_t, int, int>;
    priority_queue<V, vector<V>, greater<V>> que;
    vector<vector<int64_t>> dist(N, vector<int64_t>(MAX + 1, INF));
    S = min(S, MAX);
    dist[0][S] = 0;
    que.emplace(0, S, 0);

    auto push = [&](int v, int coin, int64_t cost) {
        if(coin >= 0 and dist[v][coin] > cost) {
            dist[v][coin] = cost;
            que.emplace(cost, coin, v);
        }
    };
    while(!que.empty()) {
        auto[cost, coin, cur] = que.top(); que.pop();
        for(auto &e : G[cur]) push(e.to, coin - e.coin, cost + e.cost);
        push(cur, min(coin + C[cur], MAX), cost + D[cur]);
    }

    for(int i = 1; i < N; ++i) cout << *min_element(dist[i].begin(), dist[i].end()) << '\n';
    return 0;
}
