#include <bits/stdc++.h>
const long long int MAX = (long long int)(1e18 + 1);
const long long int MIN = (long long int)(-1e18 - 1);
const long long int mod = (long long int)(1e9 + 7);
using namespace std;
long long int max(long long int a, long long int b, long long int c) {
  return max(max(a, b), c);
}
long long int min(long long int a, long long int b, long long int c) {
  return min(min(a, b), c);
}
long long int max(long long int a, long long int b) { return (a > b) ? a : b; }
long long int min(long long int a, long long int b) { return (a < b) ? a : b; }
long long int power(long long int a, long long int n) {
  long long int p = 1;
  while (n > 0) {
    if (n % 2) {
      p = p * a;
    }
    n >>= 1;
    a *= a;
  }
  return p;
}
long long int power_mod(long long int a, long long int n, long long int mod_) {
  long long int p = 1;
  while (n) {
    if (n % 2) {
      p = (p * a) % mod_;
    }
    n /= 2;
    a = (a * a) % mod_;
  }
  return p % mod_;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  ;
  long long int mn = MAX, mx = MIN;
  long long int n, t, m, k, i, j, sum = 0, prev, flag = 0, cnt = 0;
  long long int x = 0, y = 0, fx, diff, tot = 0, l, r;
  int TC = 1;
  while (TC--) {
    cin >> n >> k;
    x = n;
    vector<long long int> f;
    if (k > n or k >= 1000000 or k * (k + 1) / 2 > n) {
      cout << "-1";
      continue;
    }
    for (i = 1; i < sqrt(n); i++) {
      if (n % i == 0) {
        f.push_back(i);
        f.push_back(n / i);
      }
    }
    x = (long long int)(sqrt(n));
    if (x * x == n) f.push_back(x);
    sort((f).begin(), (f).end());
    l = 0, r = f.size();
    while (r - l >= 2) {
      m = (r + l) / 2;
      x = f[m];
      y = n / x - (k + 1) * k / 2;
      if (y >= 0) {
        l = m;
      } else
        r = m;
    }
    x = f[l];
    vector<long long int> ans(k);
    for (i = 0; i < k - 1; i++) ans[i] = x * (i + 1);
    ans[k - 1] = n - x * k * (k - 1) / 2;
    if (k >= 2 and ans[k - 1] > ans[k - 2])
      for (i = 0; i < k; i++) cout << ans[i] << ' ';
    else if (k < 2) {
      cout << n;
    } else {
      cout << "-1";
    }
  }
  return 0;
}

### Prompt

In cpp, your task is to solve the following problem:

You are given positive integer number n. You should create such strictly increasing sequence of k positive numbers a1, a2, ..., ak, that their sum is equal to n and greatest common divisor is maximal.

Greatest common divisor of sequence is maximum of such numbers that every element of sequence is divisible by them.

If there is no possible sequence then output -1.

Input

The first line consists of two numbers n and k (1 ≤ n, k ≤ 1010).

Output

If the answer exists then output k numbers — resulting sequence. Otherwise output -1. If there are multiple answers, print any of them.

Examples

Input

6 3


Output

1 2 3


Input

8 2


Output

2 6


Input

5 3


Output

-1

### Response

```cpp
#include <bits/stdc++.h>
const long long int MAX = (long long int)(1e18 + 1);
const long long int MIN = (long long int)(-1e18 - 1);
const long long int mod = (long long int)(1e9 + 7);
using namespace std;
long long int max(long long int a, long long int b, long long int c) {
  return max(max(a, b), c);
}
long long int min(long long int a, long long int b, long long int c) {
  return min(min(a, b), c);
}
long long int max(long long int a, long long int b) { return (a > b) ? a : b; }
long long int min(long long int a, long long int b) { return (a < b) ? a : b; }
long long int power(long long int a, long long int n) {
  long long int p = 1;
  while (n > 0) {
    if (n % 2) {
      p = p * a;
    }
    n >>= 1;
    a *= a;
  }
  return p;
}
long long int power_mod(long long int a, long long int n, long long int mod_) {
  long long int p = 1;
  while (n) {
    if (n % 2) {
      p = (p * a) % mod_;
    }
    n /= 2;
    a = (a * a) % mod_;
  }
  return p % mod_;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  ;
  long long int mn = MAX, mx = MIN;
  long long int n, t, m, k, i, j, sum = 0, prev, flag = 0, cnt = 0;
  long long int x = 0, y = 0, fx, diff, tot = 0, l, r;
  int TC = 1;
  while (TC--) {
    cin >> n >> k;
    x = n;
    vector<long long int> f;
    if (k > n or k >= 1000000 or k * (k + 1) / 2 > n) {
      cout << "-1";
      continue;
    }
    for (i = 1; i < sqrt(n); i++) {
      if (n % i == 0) {
        f.push_back(i);
        f.push_back(n / i);
      }
    }
    x = (long long int)(sqrt(n));
    if (x * x == n) f.push_back(x);
    sort((f).begin(), (f).end());
    l = 0, r = f.size();
    while (r - l >= 2) {
      m = (r + l) / 2;
      x = f[m];
      y = n / x - (k + 1) * k / 2;
      if (y >= 0) {
        l = m;
      } else
        r = m;
    }
    x = f[l];
    vector<long long int> ans(k);
    for (i = 0; i < k - 1; i++) ans[i] = x * (i + 1);
    ans[k - 1] = n - x * k * (k - 1) / 2;
    if (k >= 2 and ans[k - 1] > ans[k - 2])
      for (i = 0; i < k; i++) cout << ans[i] << ' ';
    else if (k < 2) {
      cout << n;
    } else {
      cout << "-1";
    }
  }
  return 0;
}

```