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.InputStream;
import java.io.InputStreamReader;
import java.util.Random;

public class B {
    static int n,k, mina0=Integer.MAX_VALUE, maxa0=Integer.MIN_VALUE;
    static int[] a, counts;
    
    static int solve() {
        for (int i=0; i<n; i++) {
            int a0=a[i]-k*i;
        
            if(mina0>a0) {
                mina0=a0;
            }
            if(maxa0<a0) {
                maxa0=a0;
            }
        }
        
        counts=new int[maxa0-mina0+1];
        
        for (int i=0; i<n; i++) {
            int a0=a[i]-k*i;
            counts[a0-mina0]++;
        }
        
        int best=0, besta0=-1;
        for (int i=0; i<counts.length; i++) {
            if(counts[i]>best&&i+mina0>0) {
                best=counts[i];
                besta0=i+mina0;
            }
        }
        
        return besta0;
    }
    
    
    static StringBuilder sb=new StringBuilder();
    static void parse(String l, int[] here) {
        sb.setLength(0);
        int len=l.length(), j=0;
        for (int i=0; i<len; i++) {
            char c=l.charAt(i);
            if(c==' ') {
                here[j++]=Integer.parseInt(sb.toString());
                sb.setLength(0);
            } else {
                sb.append(c);
            }
        }
        if(sb.length()>0) {
            here[j++]=Integer.parseInt(sb.toString());
        }
    }
    
    static void run_stream(InputStream ins) throws IOException {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        
        String[] s=br.readLine().split(" ");
        n=Integer.parseInt(s[0]);
        k=Integer.parseInt(s[1]);
        
        a=new int[n];
        parse(br.readLine(), a);
        
        int besta0=solve(), best=counts[besta0-mina0];
        
        sb.setLength(0);
        sb.append((n-best)+"\n");
        for (int i=0; i<n; i++) {
            int a0=a[i]-k*i;
            if(a0<besta0) {
                sb.append("+ "+(i+1)+" "+(besta0-a0));
                sb.append("\n");
            } else if(a0>besta0) {
                sb.append("- "+(i+1)+" "+(a0-besta0));
                sb.append("\n");
            }
        }
        
        System.out.println(sb.toString());
    }

    public static void main(String[] args) throws IOException {
        run_stream(System.in);
        
        //test_random();
    }


    
    static void test_random() {
        Random r=new Random();
        n=1000; k=r.nextInt(20);
        
        a=new int[n];
        for (int i=0; i<n; i++) {
            a[i]=r.nextInt(1000);
        }
        
        int besta0=solve(), best=counts[besta0-mina0], cnt=0;
        for (int i=0; i<n; i++) {
            int a0=a[i]-k*i;
            if(a0==besta0) {
                cnt++;
            }
        }
        
        if(cnt!=best) {
            System.out.println("error");
        } else {
            System.out.println("all good");
        }
    }
}
