D. N Problems During K Daystime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputPolycarp 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.InputThe 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.OutputIf 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.ExamplesInput
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

26 6

YES 1 2 4 5 6 8  
['constructive algorithms', 'greedy', 'math', '*1900']