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.ArrayList;
import java.util.Scanner;

public class B {
	Scanner in = new Scanner(System.in);

	public void run() {
		int n = in.nextInt(), k = in.nextInt();
		int[] heights = new int[n];
		
		for (int i = 0; i < n; i++) 
			heights[i] = in.nextInt();
		
		int base = 0, max = -1;
		for (int i = 0; i < n; i++) {
			int cnt = 0;
			for (int j = i + 1; j < n; j++) {
				int dist = j - i;
				if (heights[i] + k * dist == heights[j]) {
					cnt++;
				}
			}
			if (cnt > max && heights[i] - i * k > 0) {
				base = i;
				max = cnt;
			}
		}
		
		//System.out.println("base = " + base + ", max = " + max);
		int res = 0;
		ArrayList<String> list = new ArrayList<String>();
		
		for (int i = 0; i < n; i++) {
			if (i == base) continue;
			int dist = Math.abs(base - i);
			int value = heights[i];
			if (i < base) {
				value += dist * k;
			} else if (i > base) {
				value -= dist * k;
			}
			if (value < heights[base]) {
				res++;
				int x = Math.abs(value - heights[base]);
				list.add("+ " + (i+1) + " " + x);
			} else if (value > heights[base]) {
				res++;
				int x = Math.abs(value - heights[base]);
				list.add("- " + (i+1) + " " + x);
			}
		}
		System.out.println(res);
		
		for (int i = 0; i < list.size(); i++) {
			System.out.println(list.get(i));
		}
	}

	public static void main(String[] args) {
		new B().run();
	}
}

