Problem: Bankopolis is an incredible city in which all the n crossroads are located on a straight line and numbered from 1 to n along it. On each crossroad there is a bank office.

The crossroads are connected with m oriented bicycle lanes (the i-th lane goes from crossroad ui to crossroad vi), the difficulty of each of the lanes is known.

Oleg the bank client wants to gift happiness and joy to the bank employees. He wants to visit exactly k offices, in each of them he wants to gift presents to the employees.

The problem is that Oleg don't want to see the reaction on his gifts, so he can't use a bicycle lane which passes near the office in which he has already presented his gifts (formally, the i-th lane passes near the office on the x-th crossroad if and only if min(ui, vi) < x < max(ui, vi))). Of course, in each of the offices Oleg can present gifts exactly once. Oleg is going to use exactly k - 1 bicycle lane to move between offices. Oleg can start his path from any office and finish it in any office.

Oleg wants to choose such a path among possible ones that the total difficulty of the lanes he will use is minimum possible. Find this minimum possible total difficulty.

Input

The first line contains two integers n and k (1 ≤ n, k ≤ 80) — the number of crossroads (and offices) and the number of offices Oleg wants to visit.

The second line contains single integer m (0 ≤ m ≤ 2000) — the number of bicycle lanes in Bankopolis.

The next m lines contain information about the lanes.

The i-th of these lines contains three integers ui, vi and ci (1 ≤ ui, vi ≤ n, 1 ≤ ci ≤ 1000), denoting the crossroads connected by the i-th road and its difficulty.

Output

In the only line print the minimum possible total difficulty of the lanes in a valid path, or -1 if there are no valid paths.

Examples

Input

7 4
4
1 6 2
6 2 2
2 4 2
2 7 1


Output

6


Input

4 3
4
2 1 2
1 3 2
3 4 2
4 1 1


Output

3

Note

In the first example Oleg visiting banks by path 1 → 6 → 2 → 4.

Path 1 → 6 → 2 → 7 with smaller difficulity is incorrect because crossroad 2 → 7 passes near already visited office on the crossroad 6.

In the second example Oleg can visit banks by path 4 → 1 → 3.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;

public class Bank {
    static ArrayList <Data> g[] = new ArrayList [90];
    static int n, k;
    static int inf = (int) 1e8; 
    static int [][][][] mem = new int [2][82][82][82];

    static int dp(int side, int l, int r, int move) {
        if(move == (k-1)) {
            return 0;
        }
        // if(l <= 0 || l > n) return inf;
        // if(r <= 0 || r > n) return inf;
        if(mem[side][l][r][move] != -1) return mem[side][l][r][move];

        int cur = (side == 0) ? l : r;
        int ans = inf;
        if(side == 0) {
            for(Data i : g[cur]) {
                if(l < i.pos && i.pos <= r) {
                    ans = Math.min(ans, dp(0, i.pos, r, move + 1) + i.cost);
                    ans = Math.min(ans, dp(1, l + 1, i.pos, move + 1) + i.cost);
                }
            }
        } else {
            for(Data i : g[cur]) {
                if(l <= i.pos && i.pos < r) {
                    ans = Math.min(ans, dp(1, l, i.pos, move + 1) + i.cost);
                    ans = Math.min(ans, dp(0, i.pos, r - 1, move + 1) + i.cost);
                }
            }
        }
        return  mem[side][l][r][move] = ans;
    } 

    public static void main(String [] args) {
        Reader in = new Reader ();
        Writer out = new Writer ();
        n = in.nextInt();
        k = in.nextInt();

        int m = in.nextInt();
        for(int i = 0; i <= n; i++) {
            g[i] = new ArrayList <> ();
        }
        for(int i = 1; i <= m; i++) {
            int u = in.nextInt();
            int v = in.nextInt();
            int w = in.nextInt();
            g[u].add(new Data(v, w));
        }

        for(int side = 0; side <= 1; side++) {
            for(int l = 0; l < 82; l++) {
                for(int r = 0; r < 82; r++) {
                    for(int move = 0; move < 82; move++) {
                        mem[side][l][r][move] = -1;
                    }
                }
            }
        } 

        int ans = inf;
        for(int i = 1; i <= n; i++) {
            ans = Math.min(ans, dp(1, 1, i, 0));
            ans = Math.min(ans, dp(0, i, n, 0));
        }
        if(ans >= inf) ans = -1;
        System.out.println(ans);
    }
    static class Data {
        int pos, cost;
        Data () {}
        Data (int pos, int cost) {
            this.pos = pos;
            this.cost = cost;
        }
    }
    static class Reader {
        private StringTokenizer a;
        private BufferedReader b;
        Reader () {
            a = null;
            b = new BufferedReader (new InputStreamReader (System.in));
        }
        public String next () {
            while(a == null || !a.hasMoreTokens()) {
                try {
                    a = new StringTokenizer (b.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return a.nextToken();
        }
        public int nextInt() {
            return Integer.parseInt(this.next());
        }
        public long nextLong () {
            return Long.parseLong(this.next());
        }
        public double nextDouble () {
            return Double.parseDouble(this.next());
        }
        public String nextLine() {
            try {
                return b.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return "";
        }
    }
    static class Writer {
        private PrintWriter a;
        private StringBuffer b;
        Writer () {
            a = new PrintWriter (System.out);
            b = new StringBuffer ("");
        }
        public void write (Object s) {
            b.append(s);
        }
        public void writeln(Object s) {
            b.append(s).append('\n');
        }
        public void flush () {
            a.print(b);
            a.flush();
            a.close();
        }
    }
    static class Pair implements Comparator <Pair> {
        int first;
        int second;
        Pair  (int a, int b) {
            this.first = a;
            this.second = b;
        }
        Pair (Pair a) {
            this.first = a.first;
            this.second = a.second;
        }
        Pair () {}
        public String toString () {
            return "[" + first + ", " + second + "]";
        }
        public int compare (Pair a, Pair b) {
            if(a.first == b.first) {
                return a.second - b.second;
            } else {
                return a.first - b.first;
            }
        }
    }
}