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.Scanner;


public class Main {

	/**
	 * @param args
	 */
	
	public static void main(String[] args) {
		Scanner input1 = new Scanner(System.in);
		int a = input1.nextInt();
		int k = input1.nextInt();
		int[] array = new int[a];
		for (int i = 0; i < a; i++) {
			array[i] = input1.nextInt();
		}
		int count = Integer.MAX_VALUE;
		int start = 0;
		int currentMax = 0;
		for (int i = 1; i <= 1000; i++) {
		
	
			for (int j = 0; j < a; j++) {
				if (i + k*j != array[j]) {
					currentMax++;
				}
			}
			if (currentMax < count) {
				count = currentMax;
				start = i;
			}
			currentMax = 0;
		}
		System.out.println(count);
		String[] strings = new String[a];
		count = 0;
		for (int i = 0; i < a; i++) {
			if (start + i*k > array[i]) {
				strings[count] = "+ " + (i+1) + " " + Math.abs(start+i*k - array[i]); 
				count++;
			} else if (start + i*k < array[i]){
				strings[count] = "- " + (i+1) + " " + Math.abs(start+i*k - array[i]); 
				count++;
			}
		}
		
		for (int i = 0; i < count; i++) {
			System.out.println(strings[i]);
		}
	}

}

         				  		 	      	