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 C402B {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt(), k = sc.nextInt();
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = sc.nextInt();
		}
		
		int min = Integer.MAX_VALUE; int pos = -1;
		int count, w;
		ONE:for (int i = 0; i < n; i++) {
			count = 0;
			for (int j = 0; j < n; j++) {
				if (a[j] + (i - j) * k != a[i]) count++;
				w = a[i] - (i - j) * k;
				if (w <= 0) continue ONE;
			}
			if (min > count) {
				min = count;
				pos = i;
			}
		}
		
		if (min > 0 && pos != -1){
			count = 0;
			w = 0;
			String[] ans = new String[min];
			for (int i = 0; i < n; i++) {
				if (a[i] + (pos - i) * k != a[pos]){
					w = a[pos] - (pos - i) * k;
					if (a[i] > w) {
						ans[count] = "- " + (i + 1) + " " + (a[i] - w);
					} else {
						ans[count] = "+ " + (i + 1) + " " + (w - a[i]);
					}
					count++;
				}
			}
			System.out.println(count);
			for (int i = 0; i < count; i++) {
				System.out.println(ans[i]);
			}
		} else {
			System.out.println("0");
		}
		sc.close();
	}

}
