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.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Scanner;
import java.util.stream.IntStream;

/**
 * 解説通りに実装したソースコード
 * 
 * https://atcoder.jp/contests/abc164/submissions/12384200 にも参考
 */
public class Main {

	public static void main(String[] args) {
		try (Scanner scanner = new Scanner(System.in)) {
			int n = scanner.nextInt(), m = scanner.nextInt();
			int s = scanner.nextInt();
			@SuppressWarnings("unchecked")
			List<Path>[] paths = new List[n];
			IntStream.range(0, n).forEach(i -> paths[i] = new ArrayList<>());
			int[] a = new int[m];
			IntStream.range(0, m).forEach(i -> {
				int from = scanner.nextInt() - 1;
				int to = scanner.nextInt() - 1;
				a[i] = scanner.nextInt();
				long b = scanner.nextLong();
				paths[from].add(new Path(from, to, a[i], b));
				paths[to].add(new Path(to, from, a[i], b));
			});
			int[] c = new int[n], d = new int[n];
			IntStream.range(0, n).forEach(i -> {
				c[i] = scanner.nextInt();
				d[i] = scanner.nextInt();
			});
			final int maxS = Arrays.stream(a).max().getAsInt() * (n - 1);
			long[][] times = new long[n][maxS + 1];
			IntStream.range(0, n).forEach(i -> Arrays.fill(times[i], Long.MAX_VALUE));
			Queue<State> queue = new PriorityQueue<>();
			queue.add(new State(0, 0, s));
			while (!queue.isEmpty()) {
				State state = queue.poll();
				int nowS = (int) Math.min(state.s, maxS);
				if (times[state.node][nowS] > state.time) {
					times[state.node][nowS] = state.time;
					if (state.s < maxS) {
						queue.add(new State(state.node, state.time + d[state.node], state.s + c[state.node]));
					}
					for (Path path : paths[state.node]) {
						long nextTime = state.time + path.time;
						long nextS = state.s - path.cost;
						if (nextS >= 0) {
							queue.add(new State(path.to, nextTime, nextS));
						}
					}
				}
			}
			IntStream.range(1, n).mapToLong(i -> Arrays.stream(times[i]).min().getAsLong())
					.forEach(System.out::println);
		}
	}

	/**
	 * ノード間の一つのパスを表すクラス
	 */
	private static class Path {
		/** 開始ノード */
		int from;
		/** 終了ノード */
		int to;
		/** 移動コスト */
		int cost;
		/** 移動時間 */
		long time;

		/**
		 * コンストラクタ
		 * 
		 * @param from 開始ノード
		 * @param to   終了ノード
		 * @param cost 移動コスト
		 * @param time 移動時間
		 */
		Path(int from, int to, int cost, long time) {
			super();
			this.from = from;
			this.to = to;
			this.cost = cost;
			this.time = time;
		}
	}

	/**
	 * 状態を表すクラス
	 */
	private static class State implements Comparable<State> {
		/** 現在の所在ノード */
		int node;
		/** 現在までかかった時間 */
		long time;
		/** 所持金 */
		long s;

		/**
		 * コンストラクタ
		 * 
		 * @param node 現在の所在ノード
		 * @param time 現在までかかった時間
		 * @param s    所持金
		 */
		State(int node, long time, long s) {
			super();
			this.node = node;
			this.time = time;
			this.s = s;
		}

		/**
		 * 比較
		 * 
		 * @param state 比較対象
		 * @return 比較結果
		 */
		@Override
		public int compareTo(State state) {
			return Long.compare(this.s, state.s);
		}
	}
}
