#include <bits/stdc++.h>
using namespace std;
const double eps = 1e-8;
int a[100005];
int main() {
  int i, j, n, k, cnt, mmin, x, y;
  scanf("%d %d", &n, &k);
  for (i = 1; i <= n; i++) scanf("%d", &a[i]);
  mmin = INT_MAX;
  for (i = 1; i <= n; i++) {
    if (a[i] - k * (i - 1) <= 0) continue;
    cnt = 0;
    for (j = i, x = a[i]; j >= 1; j--, x -= k)
      if (a[j] != x) cnt++;
    for (j = i, x = a[i]; j <= n; j++, x += k)
      if (a[j] != x) cnt++;
    if (cnt < mmin) mmin = cnt, y = i;
  }
  printf("%d\n", mmin);
  x = a[y] - k * (y - 1);
  for (i = 1; i <= n; i++, x += k) {
    if (a[i] != x) {
      if (a[i] > x)
        printf("- %d %d\n", i, a[i] - x);
      else
        printf("+ %d %d\n", i, x - a[i]);
    }
  }
  return 0;
}

### Prompt

Create a solution in CPP for 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 double eps = 1e-8;
int a[100005];
int main() {
  int i, j, n, k, cnt, mmin, x, y;
  scanf("%d %d", &n, &k);
  for (i = 1; i <= n; i++) scanf("%d", &a[i]);
  mmin = INT_MAX;
  for (i = 1; i <= n; i++) {
    if (a[i] - k * (i - 1) <= 0) continue;
    cnt = 0;
    for (j = i, x = a[i]; j >= 1; j--, x -= k)
      if (a[j] != x) cnt++;
    for (j = i, x = a[i]; j <= n; j++, x += k)
      if (a[j] != x) cnt++;
    if (cnt < mmin) mmin = cnt, y = i;
  }
  printf("%d\n", mmin);
  x = a[y] - k * (y - 1);
  for (i = 1; i <= n; i++, x += k) {
    if (a[i] != x) {
      if (a[i] > x)
        printf("- %d %d\n", i, a[i] - x);
      else
        printf("+ %d %d\n", i, x - a[i]);
    }
  }
  return 0;
}

```