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 cf {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int k = sc.nextInt();
        int[] a = new int[n];
        int[] b = new int[n];
        int[] x = new int[1001];

        for (int i = 0; i < n; i++) {
            a[i] = sc.nextInt();
        }

        for (int i = 0; i < n; i++) {
            b[i] = a[i] - k*i;
            if (b[i] > 0) {
                x[b[i]]++;
            }
        }
        int ans = 0;
        int max = 0;
        for (int i = 0; i <= 1000; i++) {
            if (max < x[i]) {
                max = x[i];
                ans = i;
            }
        }

        int count = 0;
        for (int i = 0; i < n; i++) {
            if (b[i] != ans) {
                count++;
            }
        }

        System.out.printf("%d\n", count);
        for (int i = 0; i < n; i++) {
            if (b[i] < ans) {
                int cur = k*i + ans - a[i];
                System.out.printf("+ %d %d\n", i+1, cur);
            } else if (b[i] > ans) {
                int cur = a[i] - (k*i + ans);
                System.out.printf("- %d %d\n", i+1, cur);
            }
        }
    }
}
