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.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashSet;
import java.util.Set;
import java.util.StringTokenizer;

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);
        Task solver = new Task();
        solver.solve(1, in, out);
        out.close();
    }
}

class Task {

    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 ans = n, x = -1;
        for (int i = 0; i < n; i++) {
            int y = 0;
            int b = a[i];
            for (int j = i - 1; j >= 0; j--) {
                b -= k;
                if (b <= 0) break;
                if (a[j] != b) y++;
            }
            if (b <= 0) continue;
            b = a[i];
            for (int j = i + 1; j < n; j++) {
                b += k;
                if (a[j] != b) y++;
            }
            if (ans > y) {
                ans = y;
                x = i;
            }
        }
        out.println(ans);
        int[] na = new int[n];
        na[x] = a[x];
        for (int j = x - 1; j >= 0; j--)
            na[j] = na[j + 1] - k;
        for (int j = x + 1; j < n; j++)
            na[j] = na[j - 1] + k;
        for (int i = 0; i < n; i++) {
            if (na[i] > a[i]) {
                out.println("+ " + (i + 1) + " " + (na[i] - a[i]));
            } else if (a[i] > na[i]) out.println("- " + (i + 1) + " " + (a[i] - na[i]));
        }
    }
}

class InputReader {

    public BufferedReader  reader;
    public StringTokenizer tokenizer;

    public InputReader(InputStream stream){
        reader = new BufferedReader(new InputStreamReader(stream));
        tokenizer = null;
    }

    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

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

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

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