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 Main {
    public static void main(String[] args) {
        Scanner r = new Scanner(System.in);
        //Ingresar las medidas a la lista
        int medidas = r.nextInt();
        int coeficiente = r.nextInt();
        int lista[] = new int [medidas];
        for(int k=0;k<lista.length;k++){
        	lista[k] = r.nextInt();
        }
        //Calcular el índice fijo (el más óptimo para hacer los cortes)
        int indice_fijo = 0;
        int cortes_optimos = cortes(0,coeficiente,lista);
        for(int k=1;k<medidas;k++){
        	int cortes_actuales = cortes(k,coeficiente,lista);
        	if(cortes_actuales<cortes_optimos){
        		cortes_optimos = cortes_actuales;
        		indice_fijo = k;
        	}
        }
        //Mostrar el número de cortes óptimos
        System.out.println(cortes_optimos);
        //Determinar los cortes apartir del índice fijo
        int medida = lista[indice_fijo];
        int medida_reglamentaria;
        //Para la parte izquierda
        for(int k=0;k<indice_fijo;k++){
        	medida_reglamentaria = medida-(indice_fijo-k)*coeficiente;
        	if(lista[k]!=medida_reglamentaria){
        		if(lista[k]>medida_reglamentaria){
        			System.out.println("- "+(k+1)+" "+(lista[k]-medida_reglamentaria));
        		}
        		else{
        			System.out.println("+ "+(k+1)+" "+(medida_reglamentaria-lista[k]));
        		}
        	}
        }
        //Para la parte derecha
        for(int k=indice_fijo+1;k<medidas;k++){
        	medida_reglamentaria = medida+(k-indice_fijo)*coeficiente;
        	if(lista[k]!=medida_reglamentaria){
        		if(lista[k]>medida_reglamentaria){
        			System.out.println("- "+(k+1)+" "+(lista[k]-medida_reglamentaria));
        		}
        		else{
        			System.out.println("+ "+(k+1)+" "+(medida_reglamentaria-lista[k]));
        		}
        	}
        }
    }
    public static int cortes(int indice,int coeficiente,int lista[]){
    	int medida = lista[indice];
    	int cortes = 0;
    	if(medida-(indice*coeficiente)<=0){
    		cortes = cortes + 10*lista.length;
    	}
    	//Para la parte izquierda
    	int medida_actual;
    	for(int k=0;k<indice;k++){
    		medida_actual = lista[k];
    		if(medida_actual!=medida-((indice-k)*coeficiente)){
    			cortes = cortes+1;
    		}
    	}
    	//Para la parte derecha
    	for(int k=indice+1;k<lista.length;k++){
    		medida_actual = lista[k];
    		if(medida_actual!=medida+((k-indice)*coeficiente)){
    			cortes = cortes+1;
    		}
    	}
    	return cortes;
    }
}