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.*;
import java.util.*;

import static java.lang.Math.*;
import static java.util.Arrays.*;

public class Main {

	BufferedReader in;
	PrintWriter out;
	StringTokenizer st = new StringTokenizer("");

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

	void run() throws IOException {
		// in = new BufferedReader(new FileReader("input.txt"));
		// out = new PrintWriter("output.txt");

		if (new File("input.txt").exists())
			in = new BufferedReader(new FileReader("input.txt"));
		else
			in = new BufferedReader(new InputStreamReader(System.in));
		if (new File("output.txt").exists())
			out = new PrintWriter("output.txt");
		else
			out = new PrintWriter(System.out);

		solve();

		in.close();
		out.close();
	}

	final int maxn = 1010;

	int n, k;
	int a[] = new int[maxn];

	int getCount(int v) {
		if (a[v] - k * v <= 0)
			return n;
		int count = 0;
		for (int i = 0; i < n; i++)
			if (a[i] + k * (v - i) != a[v])
				count++;
		return count;
	}

	void solve() throws IOException {
		n = nextInt();
		k = nextInt();
		for (int i = 0; i < n; i++)
			a[i] = nextInt();
		int ans = getCount(0);
		int v = 0;
		for (int i = 1; i < n; i++) {
			int curAns = getCount(i);
			if (ans > curAns) {
				ans = curAns;
				v = i;
			}
		}
		out.println(ans);
		if (ans == n) {
			for (int i = 0; i < n; i++) {
				int need = 1 + i * k - a[i];
				if (need < 0) {
					out.println("- " + (i + 1) + " " + (-need));
				}
				if (need > 0) {
					out.println("+ " + (i + 1) + " " + (need));
				}
			}
		} else {
			for (int i = 0; i < n; i++) {
				int need = a[v] - k * (v - i) - a[i];
				if (need < 0) {
					out.println("- " + (i + 1) + " " + (-need));
				}
				if (need > 0) {
					out.println("+ " + (i + 1) + " " + (need));
				}
			}
		}
	}

	String nextToken() throws IOException {
		while (!st.hasMoreTokens())
			st = new StringTokenizer(in.readLine());
		return st.nextToken();
	}

	int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}

	long nextLong() throws IOException {
		return Long.parseLong(nextToken());
	}

	double nextDouble() throws IOException {
		return Double.parseDouble(nextToken());
	}

	String nextLine() throws IOException {
		st = new StringTokenizer("");
		return in.readLine();
	}

}
