#include <bits/stdc++.h>
using namespace std;
int h[1010];
int main() {
  int n, k;
  cin >> n >> k;
  for (int i = 1; i <= n; i++) scanf("%d", &h[i]);
  int ans = 1, de = 1, num = 1, su = 5000;
  for (int i = 1; i <= 1000; i++) {
    int w = i - k;
    de = num = 0;
    int j;
    for (j = 1; j <= n; j++) {
      w += k;
      if (w != h[j]) ++num;
      if (w > h[j]) ++de;
    }
    if (su > num) {
      ans = i;
      su = num;
    }
    if (de >= n) break;
  }
  int w = ans - k;
  int c;
  cout << su << endl;
  for (int i = 1; i <= n; i++) {
    w += k;
    c = w - h[i];
    if (c < 0) {
      c = 0 - c;
      cout << "- " << i << " " << c << endl;
    } else if (c > 0) {
      cout << "+ " << i << " " << c << endl;
    }
  }
}

### Prompt

In cpp, your task is to solve 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;
int h[1010];
int main() {
  int n, k;
  cin >> n >> k;
  for (int i = 1; i <= n; i++) scanf("%d", &h[i]);
  int ans = 1, de = 1, num = 1, su = 5000;
  for (int i = 1; i <= 1000; i++) {
    int w = i - k;
    de = num = 0;
    int j;
    for (j = 1; j <= n; j++) {
      w += k;
      if (w != h[j]) ++num;
      if (w > h[j]) ++de;
    }
    if (su > num) {
      ans = i;
      su = num;
    }
    if (de >= n) break;
  }
  int w = ans - k;
  int c;
  cout << su << endl;
  for (int i = 1; i <= n; i++) {
    w += k;
    c = w - h[i];
    if (c < 0) {
      c = 0 - c;
      cout << "- " << i << " " << c << endl;
    } else if (c > 0) {
      cout << "+ " << i << " " << c << endl;
    }
  }
}

```