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.*;
public final class trees_in_a_row_1
{
	static Scanner sc=new Scanner(System.in);
	static PrintWriter out=new PrintWriter(System.out);
	
	public static void main(String args[]) throws Exception
	{
		int n=sc.nextInt(),k=sc.nextInt();
		int[] a=new int[n];
		int[] st=new int[n];
		for(int i=0;i<n;i++)
		{
			a[i]=sc.nextInt();
		}
		int min=Integer.MAX_VALUE,minpos=0;
		int pos=0;
		while(pos<n)
		{
			boolean ans=true;
			int stp=st[pos];
			int val=a[pos];
			if(stp==-1)
			{
				pos++;
				continue;
			}
			else
			{
				int i=pos-1,j=pos+1;
				int kc=k;
				int c1=0,c2=0;
				while(i>=0)
				{
					if(val-kc<=0)
					{
						ans=false;
						break;
					}
					if(a[i]!=val-kc)
					{
						c1++;
					}
					else
					{
						st[i]=-1;
					}
					kc+=k;
					i--;
				}
				kc=k;
				while(j<n)
				{
					if(a[j]!=val+kc)
					{
						c2++;
					}
					else
					{
						st[j]=-1;
					}
					kc+=k;
					j++;
				}
				if(c1+c2<min && ans)
				{
					min=c1+c2;
					minpos=pos;
				}
				pos++;
			}
		}
		out.println(min);
		int i=minpos-1,j=minpos+1;
		int kc=k;
		while(i>=0)
		{
			if(a[i]!=a[minpos]-kc)
			{
				if(a[i]>a[minpos]-kc)
				{
					out.println("- "+(i+1)+" "+(a[i]-(a[minpos]-kc)));
				}
				else
				{
					out.println("+ "+(i+1)+" "+((a[minpos]-kc)-a[i]));
				}
			}
			kc+=k;
			i--;
		}
		kc=k;
		while(j<n)
		{
			if(a[j]!=a[minpos]+kc)
			{
				if(a[j]>a[minpos]+kc)
				{
					out.println("- "+(j+1)+" "+(a[j]-(a[minpos]+kc)));
				}
				else
				{
					out.println("+ "+(j+1)+" "+((a[minpos]+kc)-a[j]));
				}
			}
			kc+=k;
			j++;
		}
		out.close();
	}
}