#include <bits/stdc++.h>
using namespace std;
int n, k, arr[1001];
int main() {
  ios_base::sync_with_stdio(false);
  cin >> n >> k;
  for (int i = 0; i < n; ++i) cin >> arr[i];
  int p = 0;
  int mn = n - 1;
  for (int i = 1; i < n; ++i) {
    if (arr[i] <= i * k) continue;
    int take = arr[i] - (i * k);
    int cnt = 0;
    for (int j = 0; j < n; ++j) {
      if (arr[j] != take) ++cnt;
      take += k;
    }
    if (cnt < mn) {
      p = i;
      mn = cnt;
    }
  }
  cout << mn << '\n';
  int take = arr[p] - (p * k);
  for (int i = 0; i < n; ++i) {
    if (take > arr[i]) {
      cout << "+ " << (i + 1) << " " << (take - arr[i]) << '\n';
    } else if (take < arr[i]) {
      cout << "- " << (i + 1) << " " << (arr[i] - take) << '\n';
    }
    take += k;
  }
}

### 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 n, k, arr[1001];
int main() {
  ios_base::sync_with_stdio(false);
  cin >> n >> k;
  for (int i = 0; i < n; ++i) cin >> arr[i];
  int p = 0;
  int mn = n - 1;
  for (int i = 1; i < n; ++i) {
    if (arr[i] <= i * k) continue;
    int take = arr[i] - (i * k);
    int cnt = 0;
    for (int j = 0; j < n; ++j) {
      if (arr[j] != take) ++cnt;
      take += k;
    }
    if (cnt < mn) {
      p = i;
      mn = cnt;
    }
  }
  cout << mn << '\n';
  int take = arr[p] - (p * k);
  for (int i = 0; i < n; ++i) {
    if (take > arr[i]) {
      cout << "+ " << (i + 1) << " " << (take - arr[i]) << '\n';
    } else if (take < arr[i]) {
      cout << "- " << (i + 1) << " " << (arr[i] - take) << '\n';
    }
    take += k;
  }
}

```