Programmer Gleb frequently visits the IT Campus "NEIMARK" to participate in programming training sessions.

Not only is Gleb a programmer, but he is also a renowned rower, so he covers part of his journey from home to the campus by kayaking along a river. Assume that Gleb starts at point $$$0$$$ and must reach point $$$s$$$ (i.e., travel $$$s$$$ meters along a straight line). To make the challenge tougher, Gleb has decided not to go outside the segment $$$[0, s]$$$. The dimensions of the kayak can be neglected.

Gleb is a strong programmer! Initially, his power is $$$k$$$. Gleb's power directly affects the movement of his kayak. If his current power is $$$x$$$, then with one paddle stroke the kayak moves $$$x$$$ meters in the current direction. Gleb can turn around and continue moving in the opposite direction, but such a maneuver is quite challenging, and after each turn, his power decreases by $$$1$$$. The power can never become $$$0$$$ — if his current power is $$$1$$$, then even after turning it remains $$$1$$$. Moreover, Gleb cannot make two turns in a row — after each turn, he must move at least once before making another turn. Similarly, Gleb cannot make a turn immediately after the start — he must first perform a paddle stroke.

Gleb wants to reach point $$$s$$$ from point $$$0$$$ without leaving the segment $$$[0, s]$$$ and while preserving as much power as possible. Help him — given the value $$$s$$$ and his initial power $$$k$$$, determine the maximum possible power he can have upon reaching point $$$s$$$.