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.*;

public class Main {
    Scanner in = new Scanner(System.in);
    public static void main(String[] args) {
        new Main();
    }

    public Main(){
        new B().doIt();
    }
    
    class B{
        int n,k,input[];
        int[] a;
        int left(int index){
            int d = 0;
            for(int i=index-1;i>=0;i--){
                if(a[i+1]-a[i]==k)continue;
                a[i] = a[i+1]-k;
                d++;
            }
            if(a[0]<=0)return Integer.MAX_VALUE/2;
            return d;
        }
        
        int right(int index){
            int d = 0;
            for(int i=index+1;i<n;i++){
                if(a[i]-a[i-1]==k)continue;
                a[i]=a[i-1]+k;
                d++;
            }
            if(a[0]<=0)return Integer.MAX_VALUE/2;
            return d;
        }
        
        
        void left2(int index){
            for(int i=index-1;i>=0;i--){
                if(a[i+1]-a[i]==k)continue;
                int target = a[i+1]-a[i]-k;
                if(target<0)System.out.println("- "+(i+1)+" "+(-target));
                else System.out.println("+ "+(i+1)+" "+target);
                a[i] = a[i+1]-k;
            }
        }
        
        void right2(int index){
            for(int i=index+1;i<n;i++){
                if(a[i]-a[i-1]==k)continue;
                int target = a[i]-a[i-1]-k;
                if(target<0){
                    System.out.println("+ "+(i+1)+" "+              
                                                (-target));
                }
                else System.out.println("- "+(i+1)+" "+target);
                a[i] = a[i-1]+k;
            }
        }
        
        void doIt(){
            n = in.nextInt();
            k = in.nextInt();
            input = new int[n];
            int index = 0,num = Integer.MAX_VALUE;
            for(int i=0;i<n;i++)input[i] = in.nextInt();
            for(int i=0;i<n;i++){
                a = new int[n];
                for(int s=0;s<n;s++)a[s] = input[s];
                int b = left(i)+right(i);
                if(b<num){
                    num = b;
                    index = i;
                }
            }
            System.out.println(num);
            a = new int[n];
            for(int s=0;s<n;s++)a[s] = input[s];
            left2(index);
            right2(index);
        }
    }
}