Remainder of Concatenated Sequence

Consider the number formed by concatenating all integers from l to r in order, denoted as \( \overline{l(l+1)(l+2)\ldots (r-1)r} \). For example:

• For \( l=2, r=5 \), the number is \( 2345 \).
• For \( l=8, r=12 \), the number is \( 89101112 \).

Your task is to compute the remainder when this concatenated number is divided by 9.

Note: Even though the concatenated number could be very large, you can use the property that a number is congruent to the sum of its digits modulo 9.

inputFormat

The input consists of two integers l and r separated by a space.

outputFormat

Output the remainder when the concatenated number ( \overline{l(l+1)(l+2)\ldots (r-1)r} ) is divided by 9.

sample

2 5

5