#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e3 + 5;
const int mod = 1000000007;
const int INF = 0x3f3f3f3f;
const double eps = 1e-7;
long long gcd(long long a, long long b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
int arr[maxn], data[maxn];
int main() {
  int n, k;
  while (cin >> n >> k) {
    memset(data, 0, sizeof(data));
    memset(arr, 0, sizeof(arr));
    for (int i = 1; i <= n; i++) cin >> arr[i];
    int sum = 0, Max = INF;
    for (int i = 1; i <= n; i++) {
      sum = 0;
      for (int j = 1; j <= n; j++) {
        if (i == j)
          continue;
        else {
          if (arr[j] - arr[i] != k * (j - i)) sum++;
        }
      }
      if (sum < Max) {
        if (arr[i] - k * (i - 1) <= 0) continue;
        for (int j = 1; j <= n; j++) {
          int ans = arr[i] - arr[j];
          data[j] = k * (j - i) + ans;
        }
        Max = sum;
      }
    }
    cout << Max << endl;
    for (int i = 1; i <= n; i++) {
      if (data[i] > 0)
        printf("+ %d %d\n", i, data[i]);
      else if (data[i] == 0)
        continue;
      else
        printf("- %d %d\n", i, -data[i]);
    }
  }
  return 0;
}

### Prompt

Please create a solution in CPP to the following problem:

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;
const int maxn = 1e3 + 5;
const int mod = 1000000007;
const int INF = 0x3f3f3f3f;
const double eps = 1e-7;
long long gcd(long long a, long long b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
int arr[maxn], data[maxn];
int main() {
  int n, k;
  while (cin >> n >> k) {
    memset(data, 0, sizeof(data));
    memset(arr, 0, sizeof(arr));
    for (int i = 1; i <= n; i++) cin >> arr[i];
    int sum = 0, Max = INF;
    for (int i = 1; i <= n; i++) {
      sum = 0;
      for (int j = 1; j <= n; j++) {
        if (i == j)
          continue;
        else {
          if (arr[j] - arr[i] != k * (j - i)) sum++;
        }
      }
      if (sum < Max) {
        if (arr[i] - k * (i - 1) <= 0) continue;
        for (int j = 1; j <= n; j++) {
          int ans = arr[i] - arr[j];
          data[j] = k * (j - i) + ans;
        }
        Max = sum;
      }
    }
    cout << Max << endl;
    for (int i = 1; i <= n; i++) {
      if (data[i] > 0)
        printf("+ %d %d\n", i, data[i]);
      else if (data[i] == 0)
        continue;
      else
        printf("- %d %d\n", i, -data[i]);
    }
  }
  return 0;
}

```