C. Triangles
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

All that is required in this task is to find the number of triangles whose side lengths are integers in the range from $$$P$$$ to $$$Q$$$ inclusive.

For example, for $$$P=1$$$, $$$Q=2$$$, the answer will be 3 — these are the triangles with side lengths (1, 1, 1), (1, 2, 2), and (2, 2, 2).

Note: The triplet (1, 2, 2) could also be written as (2, 1, 2) or (2, 2, 1) — they all represent the same triangle.

Input

Two integers $$$P$$$ and $$$Q$$$ are given, each on a separate line ($$$1 \le P \le Q \le 2 \cdot 10^5$$$).

Output

Output a single integer — the required number of triangles.

Scoring

Solutions that work correctly for $$$Q \le 100$$$ will score at least 30 points.

Solutions that work correctly for $$$Q \le 2000$$$ will score at least 60 points.

Example
Input
1
2
Output
3
Note

Note that the answer may exceed the possible value of a 32-bit integer variable, so it is necessary to use a 64-bit integer data type (type int64 in Pascal, type long long in C++, type long in Java and C#). In Python, no additional steps are required.