The Hotel with Infinite Rooms

Source: UVa

Version: Phuoc Hung OJ Extended

Problem Statement

A hotel has infinitely many rooms, and only one group occupies the hotel at a time.

The first group has $S$ members and arrives on day $1$. A group of $k$ members stays for exactly $k$ days. On the next morning after that group leaves, a new group of $k+1$ members arrives and stays for $k+1$ days. This continues forever.

Given day $D$, counted from the first day, determine the size of the group staying in the hotel on day $D$.

Input

One line contains two integers $S$ and $D$.

Output

Print the size of the group staying in the hotel on day $D$.

Subtasks

• Subtask 1 (20%): $D\le10^5$.
• Subtask 2 (30%): $S=1$.
• Subtask 3 (50%): Full constraints: $1\le S\le10000$, $1\le D<10^{15}$.

Examples

Input

3 10

Output

5

Explanation

The group of $3$ stays on days $1$ through $3$, the group of $4$ on days $4$ through $7$, and the group of $5$ on days $8$ through $12$. Day $10$ is in the last interval, so the answer is $5$.