For a long time after the Mian Emperor created the world, the Mian Kingdom remained a wasteland. One day, the Mian Emperor decided to construct some buildings in the Mian Kingdom. According to the Mian Emperor's architectural aesthetics, a perfect building must be a rectangle on a 2D plane with positive integer side lengths, and no two distinct buildings may intersect in any way. The Mian Emperor can build any number of perfect buildings of any shape.

However, although the Mian Kingdom is very prestigious, its resources are extremely scarce. Therefore, the sum of the areas of the rectangles built by the Mian Emperor cannot exceed $S$, and the sum of their perimeters cannot exceed $C$.

Now, the Mian Emperor wants to know how many pairs $(A, B)$ satisfy the following: $1 \leq A \leq S$, $1 \leq B \leq C$, and there exists a construction scheme such that the sum of the areas of the buildings is $A$ and the sum of their perimeters is $B$.

Input

The first line contains two positive integers $S, C$.

Output

Output a non-negative integer representing the number of pairs $(A, B)$ that satisfy the conditions.

Examples

Input 1

4 10

Output 1

7

Subtasks

Task 1 (6 points): $1 \leq S, C \leq 10$

Task 2 (12 points): $1 \leq S, C \leq 10^3$

Task 3 (31 points): $1 \leq S, C \leq 6000$

Task 4 (51 points): $1 \leq S \leq 2 \times 10^5$, $1 \leq C \leq 4 \times 10^5$