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>
#define rep(i,n) for (int i = 0; i < (n); ++i)
using namespace std;
using ll = long long;
using P = pair<int,int>;

const int MAX_V = 50;
const int MAX_S = MAX_V*50+5;
const ll INF = 1e18;

struct Edge {
  int to, a, b;
  Edge(int to, int a, int b):to(to),a(a),b(b) {}
};

struct Data {
  int v, s;
  ll x;
  Data(int v, int s, ll x):v(v),s(s),x(x) {}
  bool operator<(const Data& a) const {
    return x > a.x;
  }
};

vector<Edge> g[MAX_V];
ll dist[MAX_V][MAX_S+5];

int main() {
  int n, m, s;
  cin >> n >> m >> s;
  rep(i,m) {
    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);
  }
  rep(i,n)rep(j,MAX_S+5) dist[i][j] = INF;
  s = min(s, MAX_S);
  priority_queue<Data> q;
  auto push = [&](int v, int s, ll x) {
    if (s < 0) return;
    if (dist[v][s] <= x) return;
    dist[v][s] = x;
    q.emplace(v,s,x);
  };
  vector<int> c(n), d(n);
  rep(i,n) cin >> c[i] >> d[i];
  push(0,s,0);
  while (!q.empty()) {
    Data hoge = q.top(); q.pop();
    int v = hoge.v, s = hoge.s;
    ll x = hoge.x;
    //if (dist[v][s] != x) continue;
    {
      int ns = min(s+c[v], MAX_S);
      push(v,ns,x+d[v]);
    }
    for (Edge e : g[v]) {
      push(e.to, s-e.a, x+e.b);
    }
  }
  for (int i = 1; i < n; ++i) {
    ll ans = INF;
    rep(j,MAX_S+5) {
      ans = min(ans, dist[i][j]);
    }
    cout << ans << endl;
  }
  return 0;
}
