#include <bits/stdc++.h>
using namespace std;
int main() {
  int a[10000];
  int n, k;
  while (~scanf("%d%d", &n, &k)) {
    memset(a, 0, sizeof a);
    int t = 1, ans = 0, Max = 0;
    for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
    for (int i = 1; i <= n; i++) {
      if (a[i] - (i - 1) * k <= 0) continue;
      ans = 0;
      for (int j = i; j <= n; j++) {
        int tem = a[j] - a[i];
        if (tem > 0 && tem == (j - i) * k) {
          ans++;
          if (Max < ans) {
            Max = ans;
            t = i;
          }
        }
      }
    }
    printf("%d\n", n - Max - 1);
    for (int i = 1; i <= n; i++) {
      if (t == i) continue;
      if (a[t] - a[i] != (t - i) * k) {
        int tem = a[i] + (t - i) * k;
        if (a[t] > tem) {
          printf("+ %d %d\n", i, a[t] - tem);
        } else
          printf("- %d %d\n", i, tem - a[t]);
      }
    }
  }
  return 0;
}

### Prompt

Develop a solution in cpp to the problem described below:

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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int main() {
  int a[10000];
  int n, k;
  while (~scanf("%d%d", &n, &k)) {
    memset(a, 0, sizeof a);
    int t = 1, ans = 0, Max = 0;
    for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
    for (int i = 1; i <= n; i++) {
      if (a[i] - (i - 1) * k <= 0) continue;
      ans = 0;
      for (int j = i; j <= n; j++) {
        int tem = a[j] - a[i];
        if (tem > 0 && tem == (j - i) * k) {
          ans++;
          if (Max < ans) {
            Max = ans;
            t = i;
          }
        }
      }
    }
    printf("%d\n", n - Max - 1);
    for (int i = 1; i <= n; i++) {
      if (t == i) continue;
      if (a[t] - a[i] != (t - i) * k) {
        int tem = a[i] + (t - i) * k;
        if (a[t] > tem) {
          printf("+ %d %d\n", i, a[t] - tem);
        } else
          printf("- %d %d\n", i, tem - a[t]);
      }
    }
  }
  return 0;
}

```