Jump

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.

Input

You are given the integers $n$ $(1\le n\le 2000)$ and $badStep$ $(1\le badStep\le 4000000)$.

Output

Compute and print the number of the topmost step that can be reached by Maggie.

Examples