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.util.*;
import java.lang.*;
import java.io.*;

class Pair<E extends Comparable<E>,F extends Comparable<F>> implements Comparable<Pair<E,F>>{
    E first;
    F second;
    public Pair(E first, F second){
        this.first=first;
        this.second=second;
    }
    public E getFirst(){return first;}
    public F getSecond(){return second;}
    public String toString(){
        return "<"+first.toString()+","+second.toString()+">";
    }
    public int hashCode(){
        return first.hashCode()*30011+second.hashCode()+2;
    }
    public boolean equals(Object obj) {
        if (this == obj)
            return true;
        if (obj == null)
            return false;
        if (getClass() != obj.getClass())
            return false;
        Pair another = (Pair) obj;
        return this.getFirst().equals(another.getFirst())&&this.getSecond().equals(another.getSecond());
    }

    public int compareTo(Pair<E,F> another){
        if(this.getFirst().equals(another.getFirst())){
            return this.getSecond().compareTo(another.getSecond());
        }
        return this.getFirst().compareTo(another.getFirst());
    }

}
class Edge implements Comparable<Edge>{
    Node end;
    long weight;
    public Edge(Node end, long weight){
        this.end = end;
        this.weight = weight;
    }
    public Edge(Node end){
        this.end = end;
        this.weight = 1;
    }
    public long getWeight(){
        return weight;
    }
    public Node getEnd(){
        return end;
    }
    public int compareTo(Edge another){
        if(this.getWeight()==another.getWeight()) return this.getEnd().compareTo(another.getEnd());
        else return (new Long(this.getWeight())).compareTo(new Long(another.getWeight()));
    }
    public String toString(){
        return "->"+end.toString()+"["+weight+"]";
    }
}
class Node implements Comparable<Node>{
    int id;
    List<Edge> edges;
    public Node(int id){
        this.id = id;
        this.edges = new LinkedList<>();
    }
    public void addEdge(Edge e){
        edges.add(e);
    }
    public void addEdge(Node n, long weight){
        this.addEdge(new Edge(n,weight));
    }
    public void addEdge(Node n){
        this.addEdge(n,1);
    }
    public void connect(Node n, long weight){
        edges.add(new Edge(n,weight));
    }
    public void connect(Node n){
        edges.add(new Edge(n));
    }
    public int getID(){
        return id;
    }
    public List<Edge> getEdges(){
        return edges;
    }
    public List<Node> getNeighbors(){
        LinkedList<Node> neighbors = new LinkedList<>();
        for(Edge e:this.getEdges()){
            neighbors.add(e.getEnd());
        }
        return neighbors;
    }
    public int compareTo(Node another){
        return this.getID()-another.getID();
    }
    public String toString(){
        return "N"+id;
    }
}
class Graph{
    static final long INF = 5000000000000000L;
    
    int size;
    List<Node> nodes;//nodes[i] have ID "i"
    int edgeNum;
    public Graph(int size){
        this.size = size;
        nodes = new ArrayList<>(size);
        for(int i=0;i<size;i++){
            nodes.add(new Node(i));
        }
        this.edgeNum=0;
    }
    public void addNode(){
        nodes.add(new Node(size));
        size++;
    }
    public void addDirectionalEdge(int i, int j, long w){ // i->j
        if(i>=size || j>=size)return;
        nodes.get(i).addEdge(nodes.get(j),w);
        edgeNum++;
    }
    public void addDirectionalEdge(int i, int j){ // i->j
        if(i>=size || j>=size)return;
        nodes.get(i).addEdge(nodes.get(j));
        edgeNum++;
    }
    public void addEdge(int i, int j, long w){
        addDirectionalEdge(i,j,w);
        addDirectionalEdge(j,i,w);
    }
    public void addEdge(int i, int j){
        addDirectionalEdge(i,j);
        addDirectionalEdge(j,i);
    }
    public int getSize(){
        return size;
    }
    public List<Edge> getEdges(int i){
        return nodes.get(i).getEdges();
    }
    public List<Node> getNeighbors(int i){
        return nodes.get(i).getNeighbors();
    }
    public long getDistance(int i, int j){
        long ans = INF;
        for(Edge e:this.getEdges(i)){
            if(e.getEnd().getID()==j) ans = Math.min(ans,e.getWeight());
        }
        return ans;
    }
    public long pathDistance(int[] nodes){
        long ans = 0;
        for(int n=1;n<nodes.length;n++){
            ans += this.getDistance(nodes[n-1],nodes[n]);
        }
        return ans;
    }
    public long pathDistance(Integer[] nodes){
        long ans = 0;
        for(int n=1;n<nodes.length;n++){
            ans += this.getDistance(nodes[n-1],nodes[n]);
        }
        return ans;
    }
    public long pathDistance(List<Integer> nodes){
        return pathDistance(nodes.toArray(new Integer[0]));
    }
    public List<Integer> queueDijkstra(int start, int end){
        long[] distance = new long[size];
        for(int n=0;n<size;n++) distance[n]=INF;
        distance[start]=0;
        int[] prev = new int[size];
        for(int n=0;n<size;n++) prev[n]=-1;

        PriorityQueue<Pair<Long,Integer>> A = new PriorityQueue<>();
        A.add(new Pair<>(distance[start],start));
        while(A.size()>0){
            Pair<Long,Integer> pair = A.poll();
            int u = pair.getSecond();
            if(pair.getFirst()>distance[u])continue;
            for(Edge e:getEdges(u)){
                int v = e.getEnd().getID();
                long newDistance = distance[u] + e.getWeight();
                if(distance[v]>newDistance){
                    A.remove(new Pair<>(distance[v],v));
                    distance[v] = newDistance;
                    prev[v] = u;
                    A.add(new Pair<>(distance[v],v));
                }
            }
        }
        LinkedList<Integer> ans = new LinkedList<>();
        ans.push(end);
        int cur = end;
        while(cur!=start){
            ans.push(prev[cur]);
            cur = prev[cur];
        }
        return ans;
    }
    public List<Integer> normalDijkstra(int start, int end){
        long[] distance = new long[size];
        for(int n=0;n<size;n++) distance[n]=INF;
        distance[start]=0;
        int[] prev = new int[size];
        for(int n=0;n<size;n++) prev[n]=-1;

        LinkedList<Integer> A = new LinkedList<>();
        A.add(start);
        while(A.size()>0){
            int best = A.peek();
            for(int p:A){
                if(distance[p]<distance[best]) best=p;
            }
            if(best==end) break;
            A.remove(new Integer(best));
            for(Edge e:getEdges(best)){
                int w = e.getEnd().getID();
                if(distance[w]==INF){
                    distance[w] = distance[best] + e.getWeight();
                    A.add(w);
                    prev[w] = best;
                }else if(distance[best]+e.getWeight() < distance[w]){
                    distance[w] = distance[best]+e.getWeight();
                    prev[w] = best;
                }
            }
        }
        LinkedList<Integer> ans = new LinkedList<>();
        ans.push(end);
        int cur = end;
        while(cur!=start){
            ans.push(prev[cur]);
            cur = prev[cur];
        }
        return ans;
    }
    public List<Integer> dijkstra(int start, int end){
        if(size*size < 2 * edgeNum + size * Math.log(size)) return normalDijkstra(start,end);
        else return queueDijkstra(start,end);
    }
    public long[] bellmanford(int start) throws IllegalArgumentException {
        long[] distance = new long[size];
        for(int i=0;i<size;i++) distance[i]=INF;
        distance[start]=0;
        for(int time=0;time<size-1;time++){
            for(Node u:nodes)for(Edge e:u.getEdges()){
                Node v = e.getEnd();
                if(distance[v.getID()]>distance[u.getID()]+e.getWeight()){
                    distance[v.getID()] = distance[u.getID()]+e.getWeight();
                }
            }
        }
        for(Node u:nodes)for(Edge e:u.getEdges()){
            Node v = e.getEnd();
            if(distance[u.getID()]+e.getWeight()<distance[v.getID()])
                throw new IllegalArgumentException();
        }
        return distance;
    }

    public Graph toRootedTree(int root){
        Graph tree = new Graph(size);
        LinkedList<Integer> toCheck = new LinkedList<>();
        Set checked = new HashSet<Integer>();
        toCheck.add(root);
        while(!toCheck.isEmpty()){
            int x = toCheck.pop();
            checked.add(x);
            for(Node ng : this.getNeighbors(x)){
                if(!checked.contains(ng.getID())){
                    toCheck.add(ng.getID());
                    tree.addDirectionalEdge(x,ng.getID());
                }
            }
        }
        return tree;
    }


}

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int V = sc.nextInt();
        int E = sc.nextInt();
        int P = sc.nextInt();
        int[] A = new int[E];
        int[] B = new int[E];
        long[] W = new long[E];
        for(int e=0; e<E; e++){
            A[e] = sc.nextInt()-1;
            B[e] = sc.nextInt()-1;
            W[e] = P-sc.nextLong();
        }
        Graph G = new Graph(V);
        Graph unweight = new Graph(V), reverse = new Graph(V);
        for(int e=0; e<E; e++){
            unweight.addDirectionalEdge(A[e],B[e],1);
            reverse.addDirectionalEdge(B[e],A[e],1);
        }
        long[] canGoToV = reverse.bellmanford(V-1);
        long[] canComeFrom1 = unweight.bellmanford(0);
        boolean[] valid = new boolean[V];
        for(int v=0; v<V; v++) valid[v] = (canComeFrom1[v]<500000000000000L) && (canGoToV[v]<500000000000000L);
        
        for(int e=0;e<E;e++){
            if(valid[A[e]] && valid[B[e]]) G.addDirectionalEdge(A[e],B[e],W[e]);
        }

        try{
            long[] distance = G.bellmanford(0);
            System.out.println(Math.max(0, -distance[V-1]));
        }catch(Exception e){
            System.out.println(-1);
        }
    }
}