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