Background

It is said that some people find problem descriptions too long.

Description

For any finite set $V \subset \mathbb{N}^*$, construct an undirected complete graph $G=(V, E)$, where the weight of the edge $(u, v)$ is the least common multiple $\mathrm{lcm}(u, v)$. The minimum spanning tree of $G$ is called the Least Common Tree (LCT) of $V$.

Given $L$ and $R$, find the sum of edge weights of the LCT for $V=\{L, L+1, \cdots, R\}$.

Input

The input consists of a single line containing two positive integers $L$ and $R$.

Output

Output a single positive integer representing the sum of the edge weights of $LCT(V)$.

Examples

Input 1

3 12

Output 1

126

Note 1

One possible set of edges in the LCT is $(3, 4), (3, 5), (3, 6), (3, 7), (4, 8), (3, 9), (5, 10), (3, 11), (3, 12)$.

Input 2

6022 14076

Output 2

66140507445

Input 3

13063 77883

Output 3

3692727018161

Input 4

325735 425533

Output 4

1483175252352926

Subtasks

For $100\%$ of the data, it is guaranteed that $1\le L\le R\le 10^6$ and $R-L\le 10^5$.