Little Maggie is standing at the bottom of a long flight of stairs. The bottom of the stairs has number 0, the bottommost step has number 1, the next step has number 2, and so on. The staircase is so long that Maggie is guaranteed not to reach its top.
Maggie will now perform n consecutive actions. The actions are numbered 1 through n, in order. When performing action X, Maggie chooses between two options: either he does nothing, or she jumps exactly X steps up the stairs. In other words, if Maggie starts performing action X standing on step Y, she will end it either on step Y, or on step Y+X.
For example, if n=3, Maggie will make three consecutive choices: whether or not to jump 1 step upwards, 2 steps upwards, and then 3 steps upwards.
One of the steps is broken. The number of this step is badStep. Maggie cannot jump onto this step.
You are given the integers n (1≤n≤2000) and badStep (1≤badStep≤4000000).
Compute and print the number of the topmost step that can be reached by Maggie.