Problem: There is a directed graph with N vertices numbered 1 to N and M edges. The i-th edge is directed from Vertex A_i to Vertex B_i, and there are C_i coins placed along that edge. Additionally, there is a button on Vertex N.

We will play a game on this graph. You start the game on Vertex 1 with zero coins, and head for Vertex N by traversing the edges while collecting coins. It takes one minute to traverse an edge, and you can collect the coins placed along the edge each time you traverse it. As usual in games, even if you traverse an edge once and collect the coins, the same number of coins will reappear next time you traverse that edge, which you can collect again.

When you reach Vertex N, you can end the game by pressing the button. (You can also choose to leave Vertex N without pressing the button and continue traveling.) However, when you end the game, you will be asked to pay T \times P coins, where T is the number of minutes elapsed since the start of the game. If you have less than T \times P coins, you will have to pay all of your coins instead.

Your score will be the number of coins you have after this payment. Determine if there exists a maximum value of the score that can be obtained. If the answer is yes, find that maximum value.

Constraints

* 2 \leq N \leq 2500
* 1 \leq M \leq 5000
* 1 \leq A_i, B_i \leq N
* 1 \leq C_i \leq 10^5
* 0 \leq P \leq 10^5
* All values in input are integers.
* Vertex N can be reached from Vertex 1.

Input

Input is given from Standard Input in the following format:


N M P
A_1 B_1 C_1
:
A_M B_M C_M


Output

If there exists a maximum value of the score that can be obtained, print that maximum value; otherwise, print `-1`.

Examples

Input

3 3 10
1 2 20
2 3 30
1 3 45


Output

35


Input

2 2 10
1 2 100
2 2 100


Output

-1


Input

4 5 10
1 2 1
1 4 1
3 4 1
2 2 100
3 3 100


Output

0

Solution (in JAVA):

Solution:
import java.io.IOException;
import java.io.InputStream;
import java.util.NoSuchElementException;
import java.util.Collections;
import java.util.Arrays;
import java.lang.Math;

public class Main {
	public static void main(String[] args) {
		FS reader = new FS();
		// write reader
		int N = reader.nextInt();
		int M = reader.nextInt();
		int P = reader.nextInt();
		Edge[] edges = new Edge[M];
		for (int i=0; i<M; i++) {
		    Edge e = new Edge(reader.nextInt()-1, reader.nextInt()-1, P-reader.nextInt());
		    edges[i] = e;
		}
		solver(N, M, edges);
	}
	
	public static void solver(int N, int M, Edge[] edges) {
		// write logic
		int ans = bellmanford(N, edges, 0, N-1);
		if (ans == Integer.MIN_VALUE) System.out.println(-1);
		else if (ans > 0) System.out.println(0);
		else System.out.println(-ans);
	}
	
	// Read Class
	static class FS {
		private final InputStream in = System.in;
		private final byte[] buffer = new byte[1024];
		private int ptr = 0;
		private int buflen = 0;
		private boolean hasNextByte() {
			if (ptr < buflen) {
				return true;
			} else {
				ptr = 0;
				try {
					buflen = in.read(buffer);
				} catch (IOException e) {
					e.printStackTrace();
				}
				if (buflen <= 0) {
					return false;
				}
			}
			return true;
		}
	
		private int readByte() { return hasNextByte() ? buffer[ptr++] : -1;}
		private boolean isPrintableChar(int c) {return 33 <= c && c <= 126;}
		private void skipUnprintable() {while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;}
	
		public boolean hasNext() { skipUnprintable(); return hasNextByte();}
		public String next() {
			if (!hasNext()) throw new NoSuchElementException();
			StringBuilder sb = new StringBuilder();
			int b = readByte();
			while(isPrintableChar(b)) {
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}
		public int nextInt() {
			return (int)nextLong();
		}
		public long nextLong() {
			if (!hasNext()) throw new NoSuchElementException();
			long n = 0;
			boolean minus = false;
			int b = readByte();
			if (b == '-') {
				minus = true;
				b = readByte();
			}
			if (b < '0' || '9' < b) {
				throw new NumberFormatException();
			}
			while(true) {
				if ('0' <= b && b <= '9') {
					n *= 10;
					n += b - '0';
				} else if(b == -1 || !isPrintableChar(b)) {
					return minus ? -n : n;
				} else {
					throw new NumberFormatException();
				}
				b = readByte();
			}
		}
	}
	
    static int bellmanford(int n, Edge[] edges, int s, int g) {
	    int[] distance = new int[n];
        int[] count    = new int[n];
        
        Arrays.fill(distance, Integer.MAX_VALUE);
        distance[s] = 0;

        for (int i=0; i<n-1; i++) {
            for (Edge e : edges) {
                if (distance[e.source] != Integer.MAX_VALUE && distance[e.source] + e.cost < distance[e.target]) {
                    distance[e.target] = distance[e.source] + e.cost;
                }
            }
        }
        int tmp = distance[g];
        for (int i=0; i<n-1; i++) {
            for (Edge e : edges) {
                if (distance[e.source] != Integer.MAX_VALUE && distance[e.source] + e.cost < distance[e.target]) {
                    distance[e.target] = distance[e.source] + e.cost;
                }
            }
        }
        
        // check logic
        if (tmp > distance[n-1]) return Integer.MIN_VALUE;
        else return distance[n-1];
    }

	static class Edge {
	    public int source = 0;
	    public int target = 0;
	    public int cost   = 0;
	    
	    public Edge(int source, int target, int cost) {
	        this.source = source;
	        this.target = target;
	        this.cost   = cost;
	    }
	    
	    public int compareTo(Edge e) {
	        return this.cost - e.cost;
	    }
	}
}