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 java.util.*;

public class Main {
	public static void main (String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int m = sc.nextInt();
		int s = sc.nextInt();
		int max = 50 * (n - 1);
		ArrayList<ArrayList<Cost>> graph = new ArrayList<>();
		for (int i = 0; i < n; i++) {
		    graph.add(new ArrayList<>());
		}
		for (int i = 0; i < m; i++) {
		    int a = sc.nextInt() - 1;
		    int b = sc.nextInt() - 1;
		    int c = sc.nextInt();
		    int d = sc.nextInt();
		    graph.get(a).add(new Cost(b, c, d));
		    graph.get(b).add(new Cost(a, c, d));
		}
		int[] coins = new int[n];
		int[] lates = new int[n];
		for (int i = 0; i < n; i++) {
		    coins[i] = sc.nextInt();
		    lates[i] = sc.nextInt();
		}
	    long[][] times = new long[n][max + 1];
	    for (int i = 0; i < n; i++) {
	        Arrays.fill(times[i], Long.MAX_VALUE);
	    }
	    PriorityQueue<Path> queue = new PriorityQueue<>();
	    queue.add(new Path(0, 0, s));
	    while (queue.size() > 0) {
	        Path p = queue.poll();
	        p.coin = Math.min(p.coin, max);
	        if (times[p.idx][p.coin] <= p.time) {
	            continue;
	        }
	        times[p.idx][p.coin] = p.time;
	        for (int i = p.coin - 1; i >= 0 && times[p.idx][i] > p.time; i--) {
	            times[p.idx][i] = p.time;
	        }
	        queue.add(new Path(p.idx, p.time + lates[p.idx], p.coin + coins[p.idx]));
	        for (Cost c : graph.get(p.idx)) {
	            if (c.coin > p.coin) {
	                continue;
	            }
	            queue.add(new Path(c.idx, p.time + c.time, p.coin - c.coin));
	        }
	    }
	    StringBuilder sb = new StringBuilder();
	    for (int i = 1; i < n; i++) {
	        sb.append(times[i][0]).append("\n");
	    }
	    System.out.print(sb);
	}
	
	static class Path implements Comparable<Path> {
	    int idx;
	    long time;
	    int coin;
	    
	    public Path(int idx, long time, int coin) {
	        this.idx = idx;
	        this.time = time;
	        this.coin = coin;
	    }
	    
	    public int compareTo(Path another) {
	        if (time == another.time) {
	            return 0;
	        } else if(time < another.time) {
	            return -1;
	        } else {
	            return 1;
	        }
	    }
	    
	    public String toString() {
	        return idx + ":" + time + ":" + coin;
	    }
	}
	
	static class Cost {
	    int idx;
	    int time;
	    int coin;
	    
	    public Cost(int idx, int coin, int time) {
	        this.idx = idx;
	        this.time = time;
	        this.coin = coin;
	    }
	}
}

