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.io.BufferedReader;
import java.io.FileNotFoundException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;

/**
 * #
 * 
 * @author pttrung
 */
public class D_Tinkoff_Eli {

	public static long MOD = 1000000007;
	static int[][][][] dp;
	static boolean print = false;

	public static void main(String[] args) throws FileNotFoundException {
		// PrintWriter out = new PrintWriter(new FileOutputStream(new File(
		// "output.txt")));
		PrintWriter out = new PrintWriter(System.out);
		Scanner in = new Scanner();
		int n = in.nextInt();
		int k = in.nextInt();
		int m = in.nextInt();
		ArrayList<Edge>[] map = new ArrayList[n];
		for (int i = 0; i < n; i++) {
			map[i] = new ArrayList<>();
		}
		for (int i = 0; i < m; i++) {
			int x = in.nextInt() - 1;
			int y = in.nextInt() - 1;
			int c = in.nextInt();
			map[x].add(new Edge(y, c));
			// map[y].add(new Edge(x, c));
		}
		dp = new int[n][n][n][k];
		for (int[][][] a : dp) {
			for (int[][] b : a) {
				for (int[] c : b) {
					Arrays.fill(c, -2);
				}
			}
		}
		int re = -1;
		for (int i = 0; i < n; i++) {
			// print = i == 1;
			int tmp = cal(i, i, i, k - 1, map);
			// out.println(tmp + " " + i);
			if (tmp != -1 && (re == -1 || re > tmp)) {
				re = tmp;
			}
		}
		out.println(re);
		out.close();
	}

	static int cal(int index, int min, int max, int k, ArrayList<Edge>[] map) {
		if (k == 0) {
			return 0;
		}
		if (dp[index][min][max][k] != -2) {
			return dp[index][min][max][k];
		}
		// if (print) {
		// System.out.println((index + 1) + " " + (min + 1) + " " + (max + 1));
		// }

		int re = -1;
		for (Edge e : map[index]) {
			if (e.x == index || e.x == min || e.x == max) {
				continue;
			}
			if (e.x > max) {
				if (index == max) {
					int tmp = cal(e.x, max, e.x, k - 1, map);
					if (tmp != -1) {
						tmp += e.y;
					} else {
						continue;
					}
					if (re == -1 || tmp < re) {
						re = tmp;
					}
				}
			} else if (e.x < min) {
				if (index == min) {
					int tmp = cal(e.x, e.x, min, k - 1, map);
					if (tmp != -1) {
						tmp += e.y;
					} else {
						continue;
					}
					if (re == -1 || tmp < re) {
						re = tmp;
					}
				}
			} else {
				if (e.x < index) {
					int tmp = cal(e.x, min, index, k - 1, map);
					if (tmp != -1) {
						tmp += e.y;
					} else {
						continue;
					}
					if (re == -1 || tmp < re) {
						re = tmp;
					}
				} else {
					int tmp = cal(e.x, index, max, k - 1, map);
					if (tmp != -1) {
						tmp += e.y;
					} else {
						continue;
					}
					if (re == -1 || tmp < re) {
						re = tmp;
					}
				}
			}
		}
		return dp[index][min][max][k] = re;
	}

	static class Edge {
		int x, y;

		public Edge(int x, int y) {
			super();
			this.x = x;
			this.y = y;
		}
	}

	public static int[] KMP(String val) {
		int i = 0;
		int j = -1;
		int[] result = new int[val.length() + 1];
		result[0] = -1;
		while (i < val.length()) {
			while (j >= 0 && val.charAt(j) != val.charAt(i)) {
				j = result[j];
			}
			j++;
			i++;
			result[i] = j;
		}
		return result;

	}

	public static boolean nextPer(int[] data) {
		int i = data.length - 1;
		while (i > 0 && data[i] < data[i - 1]) {
			i--;
		}
		if (i == 0) {
			return false;
		}
		int j = data.length - 1;
		while (data[j] < data[i - 1]) {
			j--;
		}
		int temp = data[i - 1];
		data[i - 1] = data[j];
		data[j] = temp;
		Arrays.sort(data, i, data.length);
		return true;
	}

	public static int digit(long n) {
		int result = 0;
		while (n > 0) {
			n /= 10;
			result++;
		}
		return result;
	}

	public static double dist(long a, long b, long x, long y) {
		double val = (b - a) * (b - a) + (x - y) * (x - y);
		val = Math.sqrt(val);
		double other = x * x + a * a;
		other = Math.sqrt(other);
		return val + other;

	}

	public static class Point implements Comparable<Point> {

		int x, y;

		public Point(int start, int end) {
			this.x = start;
			this.y = end;
		}

		@Override
		public int hashCode() {
			int hash = 5;
			hash = 47 * hash + this.x;
			hash = 47 * hash + this.y;
			return hash;
		}

		@Override
		public boolean equals(Object obj) {
			if (obj == null) {
				return false;
			}
			if (getClass() != obj.getClass()) {
				return false;
			}
			final Point other = (Point) obj;
			if (this.x != other.x) {
				return false;
			}
			if (this.y != other.y) {
				return false;
			}
			return true;
		}

		@Override
		public int compareTo(Point o) {
			return Integer.compare(x, o.x);
		}
	}

	public static class FT {

		long[] data;

		FT(int n) {
			data = new long[n];
		}

		public void update(int index, long value) {
			while (index < data.length) {
				data[index] += value;
				index += (index & (-index));
			}
		}

		public long get(int index) {
			long result = 0;
			while (index > 0) {
				result += data[index];
				index -= (index & (-index));
			}
			return result;

		}
	}

	public static long gcd(long a, long b) {
		if (b == 0) {
			return a;
		}
		return gcd(b, a % b);
	}

	public static long pow(long a, long b) {
		if (b == 0) {
			return 1;
		}
		if (b == 1) {
			return a;
		}
		long val = pow(a, b / 2);
		if (b % 2 == 0) {
			return val * val % MOD;
		} else {
			return val * (val * a % MOD) % MOD;

		}
	}

	static class Scanner {

		BufferedReader br;
		StringTokenizer st;

		public Scanner() throws FileNotFoundException {
			// System.setOut(new PrintStream(new
			// BufferedOutputStream(System.out), true));
			br = new BufferedReader(new InputStreamReader(System.in));
			// br = new BufferedReader(new InputStreamReader(new
			// FileInputStream(new File("input.txt"))));
		}

		public String next() {

			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (Exception e) {
					throw new RuntimeException();
				}
			}
			return st.nextToken();
		}

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

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

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

		public String nextLine() {
			st = null;
			try {
				return br.readLine();
			} catch (Exception e) {
				throw new RuntimeException();
			}
		}

		public boolean endLine() {
			try {
				String next = br.readLine();
				while (next != null && next.trim().isEmpty()) {
					next = br.readLine();
				}
				if (next == null) {
					return true;
				}
				st = new StringTokenizer(next);
				return st.hasMoreTokens();
			} catch (Exception e) {
				throw new RuntimeException();
			}
		}
	}
}