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
/*
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 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */

// package round236;

import java.util.Scanner;

/**
 *
 * @author Mbt
 */
public class B {

    public static void main(String[] args) {
        new Solver().solve();
    }
}

class Solver{
    int[] a= new int[1001], regions= new int[1001], regionsCount= new int[1001], firstIndex= new int[1001];
    void solve(){
        Scanner reader= new Scanner(System.in);
        int n= reader.nextInt();
        int k= reader.nextInt();
        reader.nextLine();
        
        for (int i=0; i<n; i++)
            a[i]= reader.nextInt();
        
        int nRegions=0;
        for (int i=0; i<n; i++){
            if (regions[i]==0){
                nRegions++;
                regionsCount[nRegions]++;
                regions[i]= nRegions;
                firstIndex[nRegions]= i;
            }
            for (int j=i+1; j<n; j++){
                if (regions[j]>0) continue;
                if (((a[j]-a[i])==(j-i)*k)){
                    regions[j]= nRegions;
                    regionsCount[nRegions]++;
                }
            }
        }
        
        // find max region
        int maxRegionIndex=0, maxRegionCount=0;
        for (int i=1; i<=nRegions; i++)
            if (regionsCount[i]>maxRegionCount && (a[firstIndex[i]]-firstIndex[i]*k)>0){
                maxRegionCount= regionsCount[i];
                maxRegionIndex= i;
            }
        
        System.out.printf("%d%n", n-maxRegionCount);
        int first= 0;
        
        first = a[firstIndex[maxRegionIndex]]-firstIndex[maxRegionIndex]*k;
        for (int i=0; i<n; i++){
            if (regions[i]!=maxRegionIndex){
                int diff= a[i]-(first+i*k);
                System.out.printf("%c %d %d %n", diff>0 ? '-':'+', i+1, Math.abs(diff));
            }
        }
    }
}    
