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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;
import java.util.ArrayList;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        CF_402B2 solver = new CF_402B2();
        solver.solve(1, in, out);
        out.close();
    }

    static class CF_402B2 {
        int inf = Integer.MAX_VALUE;

        public void solve(int testNumber, Scanner input, PrintWriter out) {
            ShortScanner in = new ShortScanner(input);
            int n = in.i(), k = in.i();
            int[] a = in.arr(n);

            int[] b = new int[n];
            int ans = inf;
            ArrayList<Entry> list = new ArrayList<>();
            for (int i = 1; i <= 2000; ++i) {
                b[0] = i;
                for (int j = 1; j < n; ++j) {
                    b[j] = b[j - 1] + k;
                }
                int cnt = 0;
                ArrayList<Entry> tmp = new ArrayList<>();
                for (int j = 0; j < n; ++j) {
                    if (a[j] != b[j]) {
                        cnt++;
                        if (b[j] > a[j]) tmp.add(new Entry('+', j + 1, b[j] - a[j]));
                        else tmp.add(new Entry('-', j + 1, a[j] - b[j]));
                    }
                }
                if (cnt < ans) {
                    ans = cnt;
                    list = tmp;
                }
            }

            out.println(ans);
            if (ans > 0) {
                for (Entry e : list) {
                    out.printf("%c %d %d\n", e.sign, e.a, e.b);
                }
            }
        }

        class ShortScanner {
            Scanner in;

            ShortScanner(Scanner in) {
                this.in = in;
            }

            int i() {
                return in.nextInt();
            }

            int[] arr(int n) {
                int[] a = new int[n];
                for (int i = 0; i < n; ++i) a[i] = in.nextInt();
                return a;
            }

        }

        class Entry {
            char sign;
            int a;
            int b;

            public Entry(char sign, int a, int b) {
                this.sign = sign;
                this.a = a;
                this.b = b;
            }

        }

    }
}
