D. N Problems During K Days
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Polycarp has to solve exactly $$$n$$$ problems to improve his programming skill before an important programming competition. But this competition will be held very soon, most precisely, it will start in $$$k$$$ days. It means that Polycarp has exactly $$$k$$$ days for training!

Polycarp doesn't want to procrastinate, so he wants to solve at least one problem during each of $$$k$$$ days. He also doesn't want to overwork, so if he solves $$$x$$$ problems during some day, he should solve no more than $$$2x$$$ problems during the next day. And, at last, he wants to improve his skill, so if he solves $$$x$$$ problems during some day, he should solve at least $$$x+1$$$ problem during the next day.

More formally: let $$$[a_1, a_2, \dots, a_k]$$$ be the array of numbers of problems solved by Polycarp. The $$$i$$$-th element of this array is the number of problems Polycarp solves during the $$$i$$$-th day of his training. Then the following conditions must be satisfied:

  • sum of all $$$a_i$$$ for $$$i$$$ from $$$1$$$ to $$$k$$$ should be $$$n$$$;
  • $$$a_i$$$ should be greater than zero for each $$$i$$$ from $$$1$$$ to $$$k$$$;
  • the condition $$$a_i < a_{i + 1} \le 2 a_i$$$ should be satisfied for each $$$i$$$ from $$$1$$$ to $$$k-1$$$.

Your problem is to find any array $$$a$$$ of length $$$k$$$ satisfying the conditions above or say that it is impossible to do it.

Input

The first line of the input contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le n \le 10^9, 1 \le k \le 10^5$$$) — the number of problems Polycarp wants to solve and the number of days Polycarp wants to train.

Output

If it is impossible to find any array $$$a$$$ of length $$$k$$$ satisfying Polycarp's rules of training, print "NO" in the first line.

Otherwise print "YES" in the first line, then print $$$k$$$ integers $$$a_1, a_2, \dots, a_k$$$ in the second line, where $$$a_i$$$ should be the number of problems Polycarp should solve during the $$$i$$$-th day. If there are multiple answers, you can print any.

Examples
Input
26 6
Output
YES
1 2 4 5 6 8
Input
8 3
Output
NO
Input
1 1
Output
YES
1
Input
9 4
Output
NO