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;
#define FOR(i,l,r) for(long long i=(l);i<(r);++i)
#define REP(i,n) FOR(i,0,n)
#define int long long
#define mp make_pair
#define pb push_back
#define eb emplace_back
#define _GLIBCXX_DEBUG
const int INF=1e18;
const int MAX_V=50;
const int MAX_S=50*MAX_V+3;

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

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

vector<Edge> G[MAX_V];
int dp[MAX_V][MAX_S+5];

signed 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].eb(v,a,b);
        G[v].eb(u,a,b);
    }
    vector<int> c(N),d(N);
    REP(i,N)cin>>c[i]>>d[i];
    REP(i,MAX_V)REP(j,MAX_S+5)dp[i][j]=INF;
    S=min(S,MAX_S);
    priority_queue<Data> q;
    auto push =[&](int v,int s, int x){
        if(s<0)return;
        if(dp[v][s] <= x)return;
        dp[v][s]=x;
        q.emplace(v,s,x);
    };
    push(0,S,0);
    while(!q.empty()){
        Data hoge=q.top();q.pop();
        int v=hoge.v, s=hoge.s, x=hoge.x;
        if(dp[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++){
        int ans=INF;
        REP(j,MAX_S+5){
            ans=min(ans,dp[i][j]);
        }
        cout<<ans<<endl;
    }
}
