N + NOD(N)

Source: UVa

Version: Phuoc Hung OJ Extended

Problem Statement

Consider the integer sequence $N_0,N_1,N_2,\ldots$ defined by

and, for $i>0$,

where $\operatorname{NOD}(x)$ is the number of positive divisors of $x$.

Given integers $A,B$, count the sequence values in the inclusive range $[A,B]$.

Input

The only line contains integers $A,B$.

Output

Print the number of sequence values satisfying $A\le N_i\le B$.

Subtasks

• Subtask 1 — 20%: $1\le A\le B\le10^4$.
• Subtask 2 — 30%: $1\le A\le B\le2\cdot10^5$.
• Subtask 3 — 50%: $1\le A\le B\le10^6$.

Example

Input

1 18

Output

7

Explanation

The sequence values in $[1,18]$ are $1,2,4,7,9,12,18$, so the answer is $7$.