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 javax.swing.*;
import java.util.HashMap;
import java.util.Map;
import java.util.Scanner;
import java.util.TreeMap;

/**
 * Created by rudolf on 16.03.14.
 */
public class B {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int k = sc.nextInt();
        int trees[] = new int[n];
        for(int i = 0; i < n; i++) {
            trees[i]  = sc.nextInt();
        }
        solve(k, trees);
    }

    private static void solve(int k, int[] trees) {
        int max = -1;
        int max_count = -1;
        int min_avail = Integer.MIN_VALUE;
        Map<Integer, Integer> df = new TreeMap<Integer, Integer>();
        for(int i = 0; i < trees.length; i++) {
            int diff = trees[i] - i * k;
            if(!df.containsKey(diff))
                df.put(diff, 1);
            else
                df.put(diff, df.get(diff) + 1);
        }
        for(Map.Entry<Integer, Integer> e: df.entrySet()) {
            boolean good = true;
            for(int i = 0; i < trees.length && good; i++) {
                if(i * k + e.getKey() <= 0) good = false;
            }
            if(!good) continue;
            if(max_count == -1 || max_count < df.get(e.getKey())) {
                max_count = e.getValue();
                max = e.getKey();
            }
        }
        int count = 0;
        StringBuilder sb = new StringBuilder();
        for(int i = 0; i < trees.length; i++) {
            int diff = trees[i] - i * k - max;
            if(diff != 0) {
                if(diff < 0)
                    sb.append("+ " + (i + 1) + " " + (diff * -1));
                else
                    sb.append("- " + (i + 1) + " " + diff);
                count++;
                sb.append("\n");
            }
        }
        System.out.println(count);
        System.out.println(sb.toString());
    }
}
