Addition and Multiplication

Namgyu recently learned addition and multiplication. Dohyun doubts that he learned them properly, so he made up a problem.

Given two integers $a$ and $b$ with $1 \le a < b \le 1000$, compute the following value.

$(1+2+\cdots+a) \times (1+2+\cdots+(a+1)) \times \cdots \times (1+2+\cdots+(b-1)) \times (1+2+\cdots+b)$

For every integer $k$ from $a$ to $b$, take the sum of the integers from $1$ to $k$, then multiply all of those sums together.

Namgyu cannot work this value out on his own. Write the program that computes it for him.

The first line contains two integers $a$ and $b$ separated by a space. ($1 \le a < b \le 1000$)

Print the value of the expression above. The result can get very large, so print it modulo $14579$.