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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;


public class P236B {

	/**
	 * @param args
	 * @throws IOException 
	 */
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] line1 = br.readLine().split(" ");
		int n = Integer.parseInt(line1[0]);
		int k = Integer.parseInt(line1[1]);
		String[] line2 = br.readLine().split(" ");
		int[] trees = new int[n];
		for (int i = 0; i < line2.length; i++) {
			trees[i] = Integer.parseInt(line2[i]);
		}
		ArrayList<String> minimum = minMinutes(trees, k, n);
		if(minimum.size() > 1){
			System.out.println(minimum.size()-1);
			for (int i = 0; i < minimum.size()-1; i++) {
				System.out.println(minimum.get(i));
			}
		}else{
			System.out.println(0);
		}
	}
	
	public static ArrayList<String> minMinutes(int[] trees, int k, int n){
		ArrayList<String> minimum = evaluateMinutes(trees, 0, n, k);
		for (int i = 1; i < n; i++) {
			int minMin = Integer.parseInt(minimum.get(minimum.size()-1));
			ArrayList<String> evaluation = evaluateMinutes(trees, i, n, k);
			int min = Integer.parseInt(evaluation.get(evaluation.size()-1));
			if(min != -1 && minMin > min){
				minimum = evaluation;
			}
		}
		return minimum;
	}

	private static ArrayList<String> evaluateMinutes(int[] trees, int tree, int n, int k) {
		ArrayList<String> evaluation = new ArrayList<>();
		int min = 0;
		int[] garden = new int[n];
		int i = tree;
		garden[tree] = trees[tree];
		while(i-1 >= 0){
			int diff = garden[i]-trees[i-1];
			if(diff != k){
				min++;
				garden[i-1] = garden[i] - k;
				if(garden[i-1] <= 0){
					evaluation.clear();
					evaluation.add("-1");
					return evaluation;
				}
				int change = trees[i-1] - garden[i-1];
				if(change >0){
					evaluation.add("- " + i + " " + Math.abs(change));
				}else{
					evaluation.add("+ " + i + " " + Math.abs(change));
				}
			}else{
				garden[i-1] = trees[i-1];
			}
			i--;
		}
		i = tree;
		while(i+1 < n){
			int diff = trees[i+1]-garden[i];
			if(diff != k){
				min++;
				garden[i+1] = garden[i] + k;
				int change = trees[i+1] - garden[i+1];
				if(change > 0){
					evaluation.add("- " + (i+2) + " " + Math.abs(change));
				}else{
					evaluation.add("+ " + (i+2) + " " + Math.abs(change));
				}
			}else{
				garden[i+1] = trees[i+1];
			}
			i++;
		}
		evaluation.add(""+min);
		return evaluation;
	}

}
