N Problems During K Days

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.