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.FileInputStream;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.List;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.Set;


class Graph<E extends Edge> {
    private final int n;
    private final List<E>[] g;

    public static <E extends Edge> Graph<E> create(int n) {
        ArrayList<E>[] l = new ArrayList[n];
        for (int i = 0; i < n; i++) {
            l[i] = new ArrayList<>();
        }
        return new Graph<>(n, l);
    }

    public Graph(int n, List<E>[] g) {
        this.n = n;
        this.g = g;
    }

    public void addDirectionalEdge(int u, E e) {
        g[u].add(e);
    }

    public Iterable<E> edges(int u) {
        return g[u];
    }

    public int edgeNum(int u) {
        return g[u].size();
    }

    public int size() {
        return n;
    }

    public long[] bellmanford(int start) {
        final long INF = 1L << 62;
        long[] dist = new long[n];
        Arrays.fill(dist, INF);
        dist[start] = 0;
        for (int i = 0; i < n - 1; i++) {
            for (int u = 0; u < n; u++) {
                for (Edge e : edges(u)) {
                    dist[e.to()] = Math.min(dist[e.to()], dist[u] + e.cost());
                }
            }
        }

        long[] res = Arrays.copyOf(dist, dist.length);
        for (int u = 0; u < n; u++) {
            for (Edge e : edges(u)) {
                int v = e.to();
                if (dist[u] + e.cost() < dist[v]) {
                    res[v] = -INF;
                }
            }
        }
        return res;
    }
}

class StrongConnectedComponents<E extends Edge> {
    private final Graph<E> graph;

    public StrongConnectedComponents(Graph<E> graph) {
        this.graph = graph;
    }

    public SCCResult doit() {
        int n = graph.size();
        int[] order = new TopologicalSort<>(graph).doit();
        boolean[] visited = new boolean[n];
        int sccSize = 0;
        for (int u = n - 1; u >= 0; u--) {
            if (!visited[u]) {
                dfs(u, order, visited, ++sccSize);
            }
        }
        return new SCCResult(order, sccSize);
    }

    private void dfs(int u, int[] order, boolean[] visited, int id) {
        visited[u] = true;
        order[u] = id;
        for (Edge e : graph.edges(u)) {
            if (!visited[e.to()]) {
                dfs(e.to(), order, visited, id);
            }
        }
    }

    class SCCResult {
        final int[] order;
        final int sccSize;

        public SCCResult(int[] order, int sccSize) {
            this.order = order;
            this.sccSize = sccSize;
        }

        public <E extends Edge> Graph<E> generateNewGraph(Graph<E> graph, EdgeGenerator<E> edgeGenerator) {
            final Graph<E> newGraph = Graph.create(sccSize);
            final UnionFindTree uft = new UnionFindTree(sccSize);
            for (int u = 0; u < graph.size(); u++) {
                for (E e : graph.edges(u)) {
                    int from = order[u];
                    int to = order[e.to()];
                    if (!uft.same(from, to)) {
                        newGraph.addDirectionalEdge(from, edgeGenerator.generate(to, e));
                    }
                }
            }
            return newGraph;
        }
    }
}

interface EdgeGenerator<E extends Edge> {
    E generate(int to, E originalEdge);
}

class TopologicalSort<E extends Edge> {
    private final Graph<E> graph;

    public TopologicalSort(Graph<E> graph) {
        this.graph = graph;
    }

    int index;
    boolean[] visited;

    public int[] doit() {
        final int n = graph.size();
        visited = new boolean[n];
        index = n - 1;

        int[] result = new int[n];
        for (int u = 0; u < n; u++) {
            if (!visited[u]) {
                dfs(u, result);
            }
        }
        if (index != -1) {
            throw new RuntimeException();
        }
        return result;
    }

    private void dfs(int u, int[] result) {
        visited[u] = true;
        for (Edge e : graph.edges(u)) {
            if (!visited[e.to()]) {
                dfs(e.to(), result);
            }
        }
        result[index--] = u;
    }
}

class SimpleEdge implements Edge {
    private final int to;

    public SimpleEdge(int to) {
        this.to = to;
    }

    @Override
    public int to() {
        return to;
    }

    @Override
    public long cost() {
        return 1;
    }
}

class EdgeImpl implements Edge {
    private final int to;
    private final long cost;

    public EdgeImpl(int to, long cost) {
        this.to = to;
        this.cost = cost;
    }

    @Override
    public int to() {
        return to;
    }

    @Override
    public long cost() {
        return cost;
    }
}

interface Edge {
    int to();

    long cost();
}

class UnionFindTree {
    int[] parent;
    int[] size;

    public UnionFindTree(int n) {
        parent = new int[n];
        size = new int[n];
        init();
    }

    public void init() {
        for (int i = 0; i < parent.length; i++) {
            parent[i] = i;
            size[i] = 1;
        }
    }

    public int find(int x) {
        if (parent[x] == x) return x;
        return parent[x] = find(parent[x]);
    }

    public boolean same(int x, int y) {
        return find(x) == find(y);
    }

    public void unite(int x, int y) {
        int xx = find(x), yy = find(y);
        if (xx == yy) return;
        parent[xx] = yy;
        size[yy] += size[xx];
    }

    public int getSize(int x) {
        return size[find(x)];
    }

    public int getSize(int x, int y) {
        int xx = find(x), yy = find(y);
        if (xx == yy)
            return size[xx];
        else
            return size[xx] + size[yy];
    }

    public String toString() {
        String res = "";
        res += Arrays.toString(parent) + "\n";
        res += Arrays.toString(size);
        return res;
    }
}

public class Main {
    InputStream is;

    int __t__ = 1;
    int __f__ = 0;
    int __FILE_DEBUG_FLAG__ = __f__;
    String __DEBUG_FILE_NAME__ = "src/F3";

    FastScanner in;
    PrintWriter out;

    public void solve() {
        int n = in.nextInt();
        int m = in.nextInt();
        int p = in.nextInt();

        Graph<EdgeImpl> graph = Graph.create(n);
        for (int i = 0; i < m; i++) {
            int a = in.nextInt() - 1;
            int b = in.nextInt() - 1;
            int c = in.nextInt();
            graph.addDirectionalEdge(a, new EdgeImpl(b, -(c - p)));
        }
        long[] distance = graph.bellmanford(0);
        boolean[] visited = new boolean[n];
        for (int i = 0; i < n; i++) {
            Arrays.fill(visited, false);
            boolean canArriveFromStart = canArrive(0, i, graph, visited);
            Arrays.fill(visited, false);
            boolean canArriveToGoal = canArrive(i, n - 1, graph, visited);
            if (canArriveFromStart && canArriveToGoal && distance[i] == -(1L << 62)) {
                System.out.println("-1");
                return;
            }
        }
        System.out.println(Math.max(-distance[n - 1], 0));
    }

    private boolean canArrive(int u, int goal, Graph<? extends Edge> graph, boolean[] visited) {
        if (u == goal) {
            return true;
        }
        visited[u] = true;
        for (Edge e : graph.edges(u)) {
            if (visited[e.to()]) {
                continue;
            }
            if (canArrive(e.to(), goal, graph, visited)) {
                return true;
            }
        }
        return false;
    }

    /* MOD_CALCULATION */
    static long MOD = 1000000007L;
    static long ADD(long a, long b) {
        return (a + b) % MOD;
    }

    static long SUB(long a, long b) {
        return (a - b + MOD) % MOD;
    }

    static long MULT(long a, long b) {
        return (a * b) % MOD;
    }

    static long POW(long a, long x) {
        long res = 1;
        for ( ; x > 0; x >>= 1) {
            if (x % 2 == 1) res = MULT(res, a);
            a = MULT(a, a);
        }

        return res;
    }

    static long DIV(long a, long b) {
        return MULT(a, POW(b, MOD - 2));
    }
    /* end */

    public void run() {
        if (__FILE_DEBUG_FLAG__ == __t__) {
            try {
                is = new FileInputStream(__DEBUG_FILE_NAME__);
            } catch (FileNotFoundException e) {
                // TODO 自動生成された catch ブロック
                e.printStackTrace();
            }
            System.out.println("FILE_INPUT!");
        } else {
            is = System.in;
        }
        in = new FastScanner(is);
        out = new PrintWriter(System.out);

        solve();
    }

    public static void main(final String[] args) {
        new Main().run();
    }

    class FastScanner {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public FastScanner(InputStream stream) {
            this.stream = stream;
            // stream = new FileInputStream(new File("dec.in"));

        }

        int read() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        boolean isEndline(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        int[] nextIntArray(int n) {
            int[] array = new int[n];
            for (int i = 0; i < n; i++)
                array[i] = nextInt();

            return array;
        }

        int[][] nextIntMap(int n, int m) {
            int[][] map = new int[n][m];
            for (int i = 0; i < n; i++) {
                map[i] = in.nextIntArray(m);
            }
            return map;
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        long[] nextLongArray(int n) {
            long[] array = new long[n];
            for (int i = 0; i < n; i++)
                array[i] = nextLong();

            return array;
        }

        long[][] nextLongMap(int n, int m) {
            long[][] map = new long[n][m];
            for (int i = 0; i < n; i++) {
                map[i] = in.nextLongArray(m);
            }
            return map;
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        double[] nextDoubleArray(int n) {
            double[] array = new double[n];
            for (int i = 0; i < n; i++)
                array[i] = nextDouble();

            return array;
        }

        double[][] nextDoubleMap(int n, int m) {
            double[][] map = new double[n][m];
            for (int i = 0; i < n; i++) {
                map[i] = in.nextDoubleArray(m);
            }
            return map;
        }

        String next() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        String[] nextStringArray(int n) {
            String[] array = new String[n];
            for (int i = 0; i < n; i++)
                array[i] = next();

            return array;
        }

        String nextLine() {
            int c = read();
            while (isEndline(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndline(c));
            return res.toString();
        }
    }
}