Description

In today's math class, Crash learned about the Least Common Multiple. For two positive integers $a$ and $b$, $\text{lcm}(a, b)$ denotes the smallest positive integer divisible by both $a$ and $b$. For example, $\text{lcm}(6, 8) = 24$.

After returning home, Crash was still thinking about what he learned. To study the Least Common Multiple, he drew an $n \times m$ table. Each cell contains a number, where the cell in the $i$-th row and $j$-th column contains $\text{lcm}(i, j)$.

Looking at this table, Crash thought of many questions. The one he most wants to solve is very simple: what is the sum of all the numbers in this table? When $n$ and $m$ are large, Crash cannot handle it, so he asks you to write a program to compute the answer. Since the result can be very large, Crash only wants the sum modulo $20101009$.

Input Format

The input contains one line with two integers $n$ and $m$.

Output Format

Output one positive integer, the sum of all numbers in the table modulo $20101009$.

4 5

122

Hint

Sample 1 Explanation:

The table is:

Constraints:

• For $30\%$ of the testdata, $n, m \le 10^3$.
• For $70\%$ of the testdata, $n, m \le 10^5$.
• For $100\%$ of the testdata, $1 \le n, m \le 10^7$.

Translated by ChatGPT 5