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.OutputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.io.Reader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author Vadim
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskB solver = new TaskB();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskB {
    public void solve(int testNumber, InputReader in, PrintWriter out) {
        int n = in.nextInt();
        int k = in.nextInt();
        int a[] = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = in.nextInt();
        }
        int d[] = new int[n];
        int v[] = new int[n];
        for (int i = 0; i < n; i++) {
            if(v[i] == 0 && a[i]>i*k) {
                int h = a[i];
                for (int j = i + 1; j < n; j++) {
                    h += k;
                    if (a[j] == h) {
                        d[i]++;
                        v[j] = 1;
                    }
                }
            }
        }
        int maxH = 0;
        int maxI = 0;
        for (int i = 0; i < n - 1; i++) {
            if(d[i] > maxH) {
                maxH = d[i];
                maxI = i;
            }
        }
        d[maxI] = a[maxI];
        if(maxI > 0) {
            for (int i = maxI - 1; i >= 0; i--) {
                d[i] =  d[i+1]-k;
            }
        }
        for (int i = maxI+1; i < n; i++) {
            d[i] = d[i-1]+k;
        }
        StringBuilder sb = new StringBuilder();
        int ans = 0;
        for (int i = 0; i < n; i++) {
            if(a[i] != d[i]) {
                ans++;
                if(a[i] > d[i]) {
                    sb.append("- ").append(i + 1).append(" ").append(a[i] - d[i]).append("\n");
                } else {
                    sb.append("+ ").append(i + 1).append(" ").append(d[i] - a[i]).append("\n");
                }
            }
        }
        out.println(ans);
        out.println(sb);
    }
}

class InputReader  extends BufferedReader {
    public InputReader(InputStream st) {
        super(new InputStreamReader(st));
    }

    public int nextInt() {
        try {
            int c = read();

            while (isWhiteSpace(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int ret = 0;
            while (c >= 0 && !isWhiteSpace(c)) {
                if (c < '0' || c > '9') {
                    throw new RuntimeException();
                }
                ret = ret * 10 + c - '0';
                c = read();
            }
            return ret * sgn;
        } catch (IOException e) {
            throw new RuntimeException(e);
        }
    }

    public String readLine() {
        try {
            return super.readLine();
        } catch (IOException e) {
            return null;
        }
    }


    static boolean isWhiteSpace(int c) {
        return c >= 0 && c <= 32;
    }



}
