Educational Codeforces Round 20 C. Maximal GCD

C. Maximal GCD

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

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
暴力枚举，k个数都是n的因子
 n - s > (k - 1)·d.然后从d枚举到n/d就好了，这个思路我是想不到的，听打神讲的，然而我还写不出来，抄了大神的代码，CF这样很好啊。帮助小白进阶，从哪里开始枚举
自己要想清楚

#include <cstdio>
typedef long long ll;
int main()
{
    ll n, k;
    scanf("%lld%lld", &n, &k);
    if (k > (ll)1e8)
    {
        printf("-1
");
        return 0;
    }
    ll b = n / (k * (k + 1) / 2);
    if (b == 0)
    {
        printf("-1
");
        return 0;
    }
    ll r = 1;
    for (ll x = 1; x * x <= n; x++)
    {
        if (n % x != 0) continue;
        if (x <= b && x > r) r = x;
        if (n / x <= b && n / x > r) r = n / x;
    }
    for (int i = 1; i < k; i++)
        printf("%lld ", r * i);
    n -= r * k * (k - 1) / 2;
    printf("%lld
", n);

    return 0;
}