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.*;
import java.io.*;

public class Main {

	public static void main(String[] args) {
		
		Scan scan = new Scan();
		int n,k;
		n = scan.nextInt();
		k = scan.nextInt();
		int[] trees = new int[n];
		for(int i=0;i<n;i++) trees[i] = scan.nextInt();
		
		int minStart=1,minVal = Integer.MAX_VALUE,now;
		
		for(int i=1;i<=1000;i++){
			now = 0;
			for(int j=0;j<n;j++){
				now += (Math.abs(i+j*k-trees[j])==0)? 0 : 1;
			}
			if(now < minVal){
				minStart = i;
				minVal = now;
			}
		}
		
		System.out.println(minVal);
		for(int i=0;i<n;i++){
			int target = minStart+i*k;
			if(target == trees[i]) continue;
			else if(target > trees[i]) System.out.println("+ "+(i+1)+" "+(target-trees[i]));
			else System.out.println("- "+(i+1)+" "+(trees[i]-target));
		}
		
	}

}

class Scan{

	BufferedReader buffer;
	StringTokenizer tok;

	public Scan(){
		buffer = new BufferedReader(new InputStreamReader(System.in));
	}

	boolean hasNext(){
		while(tok == null || !tok.hasMoreElements()){
			try{
				tok = new StringTokenizer(buffer.readLine());
			}catch(Exception e){
				return false;
			}
		}
		if(tok == null) return false;
		return true;
	}

	String next(){
		if(hasNext()) return tok.nextToken();
		return null;
	}

	String nextLine(){
		if(hasNext()) return tok.nextToken("\n\r");
		return null;
	}

	int nextChar(){
		try{
			return buffer.read();
		}catch(Exception e){
		}
		return -1;
	}

	int nextInt(){
		return Integer.parseInt(next());
	}

	long nextLong(){
		return Long.parseLong(next());
	}

	double nextDouble(){
		return Double.parseDouble(next());
	}

}