The Queen of England has n trees growing in a row in her garden. At that, the i-th (1 ≤ i ≤ n) tree from the left has height ai meters. Today the Queen decided to update the scenery of her garden. She wants the trees' heights to meet the condition: for all i (1 ≤ i < n), ai + 1 - ai = k, where k is the number the Queen chose.

Unfortunately, the royal gardener is not a machine and he cannot fulfill the desire of the Queen instantly! In one minute, the gardener can either decrease the height of a tree to any positive integer height or increase the height of a tree to any positive integer height. How should the royal gardener act to fulfill a whim of Her Majesty in the minimum number of minutes?

Input

The first line contains two space-separated integers: n, k (1 ≤ n, k ≤ 1000). The second line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 1000) — the heights of the trees in the row. 

Output

In the first line print a single integer p — the minimum number of minutes the gardener needs. In the next p lines print the description of his actions. 

If the gardener needs to increase the height of the j-th (1 ≤ j ≤ n) tree from the left by x (x ≥ 1) meters, then print in the corresponding line "+ j x". If the gardener needs to decrease the height of the j-th (1 ≤ j ≤ n) tree from the left by x (x ≥ 1) meters, print on the corresponding line "- j x".

If there are multiple ways to make a row of trees beautiful in the minimum number of actions, you are allowed to print any of them.

Examples

Input

4 1
1 2 1 5


Output

2
+ 3 2
- 4 1


Input

4 1
1 2 3 4


Output

0
import com.sun.org.apache.xerces.internal.impl.dv.xs.IntegerDV;
import com.sun.org.apache.xerces.internal.impl.xpath.regex.Match;

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


public class Main {
    MyScanner cin = new MyScanner(System.in);
    PrintWriter cout = new PrintWriter(System.out);

    int inf = (int)2e9;

    private void run() throws FileNotFoundException {
        //MyScanner cin = new MyScanner(new FileReader("wheel.in"));
        //PrintWriter cout = new PrintWriter(new File("wheel.out"));
        int i, n = cin.nextInt(), k = cin.nextInt(), m = 0, y;
        int[] a = new int[1001], b = new int[1001];
        for (i = 1; i <= n; i++){
            a[i] = cin.nextInt();
        }
        for (i = 1; i <= n; i++){
            y = a[i] - k * (i - 1);
            if (y > 0){
                b[y]++;
                if (y > m) m = y;
            }
        }
        for (y = 1, i = 2; i <= m; i++) if (b[i] > b[y]) y = i;
        cout.println(n - b[y]);
        for (i = 1; i <= n; i++, y += k){
            if (y > a[i]) cout.println("+ " + i + " " + (y - a[i]));
            if(y < a[i]) cout.println("- " + i + " " + (a[i] - y));
        }
        cout.close();
    }

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

    class MyScanner {
        BufferedReader br;
        StringTokenizer st;
        public MyScanner(FileReader in){
            br = new BufferedReader(in);
        }
        public MyScanner(InputStream in) {
            br = new BufferedReader(new InputStreamReader(in));
        }

        String next(){
            while(st == null || !st.hasMoreElements()){
                try{
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e){
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        String tmp = "";
        int nextInt(){return Integer.parseInt(next());}
        double nextDouble(){return Double.parseDouble(next());}
        long nextLong(){return Long.parseLong(next());}

        String nextLine(){
            String str = "";
            try{
                str = br.readLine();
            } catch (IOException e){
                e.printStackTrace();
            }
            return str;
        }
    }
}
