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
#include <bits/stdc++.h>
using namespace std;
int main() {
  int N, K;
  scanf("%d %d", &N, &K);
  int a[N];
  for (int i = 0; i < N; i++) scanf("%d", &a[i]);
  int arr[N], pos[N];
  int cnt = 99999;
  for (int i = 0; i < N; i++) {
    int t_arr[N], t_pos[N];
    int ptr = 0;
    bool neg = false;
    for (int j = 0; j < N; j++) {
      if (i == j) continue;
      int t_val = a[i] + ((j - i) * K) - a[j];
      if (t_val != 0) {
        t_arr[ptr] = t_val;
        t_pos[ptr] = (j + 1);
        ptr++;
        if ((t_val + a[j]) <= 0) neg = true;
      }
    }
    if (!neg && ptr < cnt) {
      cnt = ptr;
      for (int j = 0; j < cnt; j++) {
        arr[j] = t_arr[j];
        pos[j] = t_pos[j];
      }
    }
  }
  printf("%d\n", cnt);
  for (int i = 0; i < cnt; i++) {
    if (arr[i] < 0)
      printf("%c %d %d\n", '-', pos[i], -arr[i]);
    else
      printf("%c %d %d\n", '+', pos[i], arr[i]);
  }
  return 0;
}
