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
/**
 * Created by Anna.Skobaneva on 3/16/14.
 */

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class TaskB {

    StringTokenizer st;
    BufferedReader in;
    PrintWriter out;

    public static void main(String[] args) throws NumberFormatException,
            IOException {
        TaskB solver = new TaskB();
        solver.open();
        long time = System.currentTimeMillis();
        solver.solve();
        if (!"true".equals(System.getProperty("ONLINE_JUDGE"))) {
            System.out.println("Spent time: "
                    + (System.currentTimeMillis() - time));
            System.out.println("Memory: "
                    + (Runtime.getRuntime().totalMemory() - Runtime
                    .getRuntime().freeMemory()));
        }
        solver.close();
    }

    public void open() throws IOException {
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        //in = new BufferedReader(new FileReader("input.txt"));
        //out = new PrintWriter(new FileWriter("output.txt"));
    }

    public String nextToken() throws IOException {
        while (st == null || !st.hasMoreTokens()) {
            String line = in.readLine();
            if (line == null)
                return null;
            st = new StringTokenizer(line);
        }
        return st.nextToken();
    }

    public int nextInt() throws NumberFormatException, IOException {
        return Integer.parseInt(nextToken());
    }

    public long nextLong() throws NumberFormatException, IOException {
        return Long.parseLong(nextToken());
    }

    public double nextDouble() throws NumberFormatException, IOException {
        return Double.parseDouble(nextToken());
    }

    boolean hasMoreTokens() throws IOException {
        while (st == null || !st.hasMoreTokens()) {
            String line = in.readLine();
            if (line == null)
                return false;
            st = new StringTokenizer(line);
        }
        return true;
    }

    public void solve() throws NumberFormatException, IOException {
        int n = nextInt();
        int k = nextInt();
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = nextInt();
        }

        int maxRow = 1;
        int baseNum = 0;
        for (int i = 0; i < n; i++) {
            if (a[i] - k * i < 1) continue;
            int cntRow = 1;
            for (int j = 0; j <= i - 1; j++) {
                if (a[j] + k * (i - j) == a[i]) cntRow++;
            }
            for (int j = i + 1; j < n; j++) {
                if (a[j] - k * (j - i) == a[i]) cntRow++;
            }
            if (cntRow > maxRow) {
                maxRow = cntRow;
                baseNum = i;
            }
        }

        out.println(n - maxRow);
        for (int i = 0; i < n; i++) {
            if (i == baseNum) continue;
            if (i < baseNum && a[i] + k * (baseNum - i) == a[baseNum]) continue;
            if (i > baseNum && a[i] - k * (i - baseNum) == a[baseNum]) continue;
            if (i< baseNum) {
                int tmp = a[baseNum] - k * (baseNum - i) - a[i];
                if (tmp > 0)  {
                    out.println("+ "+(i+1)+" "+tmp);
                }   else {
                    out.println("- "+(i+1)+" "+(-tmp));
                }
            } else {
                int tmp = a[baseNum] + k * (i - baseNum) - a[i];
                if (tmp > 0)  {
                    out.println("+ "+(i+1)+" "+tmp);
                }   else {
                    out.println("- "+(i+1)+" "+(-tmp));
                }
            }
        }
    }

    public void close() {
        out.flush();
        out.close();
    }
}
