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.awt.Point;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.List;
import java.util.StringTokenizer;

public class Main
{
  static BufferedReader reader;
  static StringTokenizer tokenizer;
  static PrintWriter writer;
  
  static int nextInt() throws IOException
  {
    return Integer.parseInt(nextToken());
  }
  
  static long nextLong() throws IOException
  {
    return Long.parseLong(nextToken());
  }
  
  static double nextDouble() throws IOException
  {
    return Double.parseDouble(nextToken());
  }
  
  static boolean eof = false;
  
  static String nextToken() throws IOException
  {
    while (tokenizer == null || !tokenizer.hasMoreTokens())
    {
      tokenizer = new StringTokenizer(reader.readLine());
    }
    return tokenizer.nextToken();
  }
  
  public static void main(String[] args) throws IOException
  {
    tokenizer = null;
    reader = new BufferedReader(new InputStreamReader(System.in));
    writer = new PrintWriter(System.out);
    banana();
    reader.close();
    writer.close();
  }
  
  public static class P
  {
    public int y;
    public double x;
    public boolean beg;
    
    P(double _x, int _y, boolean _beg)
    {
      beg = _beg;
      x = _x;
      y = _y;
    }
  }
  
  static void banana() throws IOException
  {
    int n = nextInt();
    int k = nextInt();
    
    int a[] = new int[n];
    for (int i = 0 ; i < n; ++i)
      a[i] = nextInt();
    int c[] = new int[n];
    int min = n;
    for (int i = 0 ; i < n; ++i)
    {
      int b[] = new int[n];
      
      for (int j = 0 ; j < n; ++j)
        b[j] = a[i] + (j-i) * k;
      
      boolean isValid = true;
      for (int j = 0; j < n; ++j)
        if (b[j] <= 0)
          isValid = false;
      
      if (isValid)
      {
        int curMin = 0;
        for (int j = 0; j < n; ++j)
          if (b[j] != a[j])
            ++curMin;
        
        if (curMin < min)
        {
          for (int j = 0 ; j <n; ++j)
            c[j] = b[j];
          min = curMin;
        }
      }
    }
    System.out.println(min);
    for (int i = 0; i < n; ++i)
    {
      if (c[i] > a[i])
      {
        System.out.println("+ " + (i+1) + " " + (c[i] - a[i]));
      }
      if (c[i] < a[i])
      {
        System.out.println("- " + (i+1) + " " + (a[i] - c[i]));
      }
    }
    
  }
}