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, ..., 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} ≤ 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 ≤ n ≤ 10^9, 1 ≤ k ≤ 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, ..., 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
# AC
import sys


class Main:
    def __init__(self):
        self.buff = None
        self.index = 0

    def next(self):
        if self.buff is None or self.index == len(self.buff):
            self.buff = self.next_line()
            self.index = 0
        val = self.buff[self.index]
        self.index += 1
        return val

    def next_line(self, _map=str):
        return list(map(_map, sys.stdin.readline().split()))

    def next_int(self):
        return int(self.next())

    def solve(self):
        n = self.next_int()
        k = self.next_int()
        rs = []
        low = 1
        high = n + 1
        for i in range(0, k):
            kk = k - i
            high1 = high
            low1 = low
            while high1 - low1 > 1:
                mid = (low1 + high1) // 2
                if self.test_low(mid, n, kk):
                    low1 = mid
                else:
                    high1 = mid
            high2 = high
            low2 = low1
            while high2 - low2 > 1:
                mid = (low2 + high2) // 2
                if self.test_high(mid, n, kk):
                    low2 = mid
                else:
                    high2 = mid

            if not self.test_low(low1, n, kk) or not self.test_high(low2, n, kk):
                print('NO')
                return
            rs.append(low1)
            low = rs[-1] + 1
            high = rs[-1] * 2 + 1
            n -= rs[-1]
        print('YES')
        print(' '.join([str(x) for x in rs]))

    def test_low(self, d, n, k):
        return (2 * d + k - 1) * k // 2 <= n

    def test_high(self, d, n, k):
        return k >= 33 or (2 ** k - 1) * d >= n


if __name__ == '__main__':
    Main().solve()
