Problem: Petya sometimes has to water his field. To water the field, Petya needs a tank with exactly V ml of water.

Petya has got N tanks, i-th of them initially containing ai ml of water. The tanks are really large, any of them can contain any amount of water (no matter how large this amount is).

Also Petya has got a scoop that can contain up to K ml of water (initially the scoop is empty). This scoop can be used to get some water from some tank, and after that pour it all into some tank (it is impossible to get water from multiple tanks without pouring it, or leave some water in the scoop when pouring it). When Petya tries to get some water from a tank, he gets min(v, K) water, where v is the current volume of water in the tank.

Is it possible to obtain a tank with exactly V ml of water using these operations? If it is possible, print a sequence of operations that allows to do it. If there are multiple ways to obtain needed amount of water in some tank, print any of them.

Input

The first line contains 3 integers: N (2 ≤ N ≤ 5000), K (1 ≤ K ≤ 5000), and V (0 ≤ V ≤ 109) — the number of tanks, the maximum volume of water the scoop can contain, and the required amount of water in some tank, respectively.

The second line contains N integers ai (0 ≤ ai ≤ 105), where ai is initial volume of water in i-th tank.

Output

If it is impossible to obtain a tank with exactly V ml of water, print NO. 

Otherwise print YES in the first line, and beginning from the second line, print the sequence of operations in the following format: 

Each line has to contain 3 numbers denoting a compressed operation: "cnt x y" (1 ≤ cnt ≤ 109, 1 ≤ x, y ≤ N), where x is the index of the tank where we get water, y is the index of the tank where we pour water, and cnt is the number of times we transfer water from tank x to tank y. 

The number of these lines must not exceed N + 5.

Examples

Input

2 3 5
2 3


Output

YES
1 2 1


Input

2 3 4
2 3


Output

NO


Input

5 2 0
1 3 5 7 9


Output

YES
2 2 1
3 3 1
4 4 1
5 5 1

Solution (in JAVA):

Solution:
//package com.company;

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

public class Main {
    public static void main(String[] args) throws IOException {
        MyScanner sc = new MyScanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        Tanks.solve(sc, pw);
        pw.close();
    }
    //http://codeforces.com/problemset/problem/920/D
    public static class Tanks {
        static int N, K;
        static int V;
        static int[] a;
        static int[] remainder;
        static int sum;
        static int[][] dp;
        static int[][] from;
        static int[] use;
        static int cnt;
        static int unuse;
        static int mustuse;
        static int move;
        public static void solve(MyScanner sc, PrintWriter pw) throws IOException {
            N = sc.nextInt(); K = sc.nextInt(); V = sc.nextInt();
            a = new int[N];
            remainder = new int[N];
            dp = new int[N + 1][K + 1];
            from = new int[N + 1][K + 1];
            use = new int[N];
            sum = 0;
            cnt = 0;
            for (int i = 0; i < N; i++) {
                a[i] = sc.nextInt();
                remainder[i] = (int)a[i] % K;
                sum += a[i];
            }
            move = (V - (V % K)) / K;
            if (solve() == -1) {
                pw.println("NO");
                return;
            }
            pw.println("YES");
            if (cnt == 0) {
                if (a[0] != 0) {
                    print(roundup(a[0], K), 0, 1, pw);
                }
                a[1] += a[0];
                a[0] = 0;
                unuse = 1;
                mustuse = 0;
                use[0] = 1;
            } else if (cnt == N) {
                if (a[0] != 0) {
                    print(roundup(a[0], K), 0, 1, pw);
                }
                a[1] += a[0];
                a[0] = 0;
                unuse = 0;
                mustuse = 1;
                use[0] = 0;
            }

            int waterInUse = 0;
            for (int i = 0; i < N; i++) {
                if (a[i] == 0) continue;
                if (use[i] == 1) {
                    waterInUse += a[i];
                    if (i != mustuse) {
                        print(roundup(a[i], K), i, mustuse, pw);
                    }
                } else {
                    if (i != unuse) {
                        print(roundup(a[i], K), i, unuse, pw);
                    }
                }
            }
            if (waterInUse > V) {
                print(roundup(waterInUse - V, K), mustuse, unuse, pw);
            } else if (waterInUse < V) {
                print(roundup(V - waterInUse, K), unuse, mustuse, pw);
            }


        }
        public static void print(int c, int from, int to, PrintWriter pw) {
            pw.println(c + " " + (from+1) + " " + (to+1));
        }
        public static int roundup(int a, int k) {
            if (a % k == 0) return a / k;
            return a / k + 1;
        }

        public static int solve(){
            if (sum < V) {
                return -1;
            }
            dp[0][0] = 1;
            for (int i = 0; i < N; i++) {
                for (int j = 0; j < K; j++) {
                    if (dp[i][j] == 1) {
                        dp[i+1][(j+remainder[i])%K] = 1;
                        from[i+1][(j+remainder[i])%K] = j;
                        dp[i+1][j] = 1;
                        from[i+1][j] = j;
                    }
                }
            }
            if (dp[N][(int)V % K] != 1) {
                return -1;
            }
            int ff = (int)V % K;
            for (int i = N; i > 0; i--) {
                int nxt = from[i][ff];
                if (nxt != ff) {
                    use[i - 1] = 1;
                    mustuse = i - 1;
                    cnt++;
                } else {
                    unuse = i - 1;
                }
                ff = nxt;
            }
            return 1;
        }
    }



    static class MyScanner {
        StringTokenizer st;
        BufferedReader br;

        public MyScanner(InputStream s){  br = new BufferedReader(new InputStreamReader(s));}

        public MyScanner(FileReader s) throws FileNotFoundException {br = new BufferedReader(s);}

        public String next() throws IOException
        {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

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

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

        public String nextLine() throws IOException {return br.readLine();}

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

        public boolean ready() throws IOException {return br.ready();}
    }
}