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 java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Comparator;
import java.util.StringTokenizer;

/**
 * Created with IntelliJ IDEA.
 * User: AUtemuratov
 * Date: 07.04.14
 * Time: 15:43
 * To change this template use File | Settings | File Templates.
 */
public class Main {
    static int m[] = new int[1111];
    static FastReader fr = new FastReader(new BufferedReader(new InputStreamReader(System.in)));
    static PrintWriter pw = new PrintWriter(System.out);
    static int max = Integer.MIN_VALUE;
    static int min = Integer.MAX_VALUE;
    static int sum,cnt,n,k;
    static String s;
    public static void main(String[] args) throws Exception {
        n = fr.nextInt();
        k = fr.nextInt();

        for (int i=1; i<=n; i++) {
            m[i] = fr.nextInt();
        }

        int a[] = new int[1111];
        int b[] = new int[1111];

        for (int h=1; h<=1000; h++) {
            for (int i=1, j=h; i<=n; i++,j+=k) {
                a[i] = j;
            }
            int t = matches(a);
            if (t>max) {
                max = t;
                b = a.clone();
            }
        }

        pw.println(n-max);
        for (int i=1; i<=n; i++) {
            if (m[i]<b[i]) {
                pw.println("+ " + i + " " + (b[i]-m[i]));
            } else if (m[i]>b[i]) {
                pw.println("- " + i + " " + (m[i]-b[i]));
            }
        }


        pw.close();
    }

    private static int matches(int []a) {
        int cnt = 0;
        for (int i=1; i<=n; i++) {
            if (m[i]==a[i]) {
                cnt++;
            }
        }
        return cnt;
    }

}


class FastReader {

    BufferedReader bf;
    StringTokenizer tk = null;
    String DELIM = " ";

    public FastReader(BufferedReader bf) {
        this.bf = bf;
    }

    public String nextToken() throws Exception {

        if(tk==null || !tk.hasMoreTokens()) {
            tk = new StringTokenizer(bf.readLine(),DELIM);
        }
        return tk.nextToken();
    }

    public int nextInt() throws Exception {
        return Integer.parseInt(nextToken());
    }

    public int nextLong() throws Exception {
        return Integer.parseInt(nextToken());
    }

    public int nextDouble() throws Exception {
        return Integer.parseInt(nextToken());
    }
}
