#include <bits/stdc++.h>
using namespace std;
const int MOD = 1e9 + 7, INF = INT_MAX;
const long long LINF = LLONG_MAX;
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n, i, j, k, ans = INF, st;
  cin >> n >> k;
  int a[n];
  for (i = 0; i < n; i++) cin >> a[i];
  for (i = 1; i < 10001; i++) {
    int x = 0, z = i;
    for (j = 0; j < n; j++) {
      if (a[j] != z) x++;
      z += k;
    }
    if (ans > x) {
      ans = x;
      st = i;
    }
  }
  cout << ans << endl;
  for (i = 0; i < n; i++) {
    if (a[i] > st)
      cout << "-"
           << " " << i + 1 << " " << a[i] - st << endl;
    else if (a[i] < st)
      cout << "+"
           << " " << i + 1 << " " << st - a[i] << endl;
    st += k;
  }
}

### Prompt

Please provide a cpp coded solution 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;
const int MOD = 1e9 + 7, INF = INT_MAX;
const long long LINF = LLONG_MAX;
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n, i, j, k, ans = INF, st;
  cin >> n >> k;
  int a[n];
  for (i = 0; i < n; i++) cin >> a[i];
  for (i = 1; i < 10001; i++) {
    int x = 0, z = i;
    for (j = 0; j < n; j++) {
      if (a[j] != z) x++;
      z += k;
    }
    if (ans > x) {
      ans = x;
      st = i;
    }
  }
  cout << ans << endl;
  for (i = 0; i < n; i++) {
    if (a[i] > st)
      cout << "-"
           << " " << i + 1 << " " << a[i] - st << endl;
    else if (a[i] < st)
      cout << "+"
           << " " << i + 1 << " " << st - a[i] << endl;
    st += k;
  }
}

```