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.util.InputMismatchException;
import java.util.ArrayList;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.List;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.util.StringTokenizer;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
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 {
    class Action {
        int id;
        int change;
    }

    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();
        List<Action> res = null;
        for (int i = 1; i <= 1000; ++i) {
            List<Action> tmp = findChanges(i, k, a);
            if (res == null || res.size() > tmp.size())
                res = tmp;
        }
        out.println(res.size());
        for (Action x : res)
            out.println((x.change < 0 ? "- ":"+ ") + x.id + " " + Math.abs(x.change));
    }

    private List<Action> findChanges(int x, int k, int[] a) {
        List<Action> res = new ArrayList<>();
        for (int i = 0; i < a.length; ++i) {
            Action tmp = new Action();
            tmp.change = x + i * k - a[i];
            tmp.id = i + 1;
            if (tmp.change != 0) res.add(tmp);
        }
        return res;
    }
}

class InputReader {
    BufferedReader in;
    StringTokenizer st;

    public InputReader(InputStream stream) {
        in = new BufferedReader(new InputStreamReader(stream));
        eat("");
    }

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

    public String next() {
        while (!st.hasMoreTokens())
            eat(nextLine());
        return st.nextToken();
    }

    public String nextLine() {
        try {
            return in.readLine();
        } catch (IOException e) {
            throw new InputMismatchException();
        }
    }

    public void eat(String str) {
        if (str == null) throw new InputMismatchException();
        st = new StringTokenizer(str);
    }
}

