Substring Digit Sum

Given a string constructed by concatenating, in order, 1 copy of 1, 2 copies of 2, 3 copies of 3, 4 copies of 4, 5 copies of 5, 6 copies of 6, 7 copies of 7, 8 copies of 8, 9 copies of 9, 10 copies of 10, and so on, your task is to compute the sum of the digits from the l-th to the r-th position (1-indexed) in the resulting string.

For example, the beginning of the string is:

1
22
333
4444
55555
...

If we list the digits: 1,2,2,3,3,3,4,4,4,4,... then for input l = 1 and r = 5, the substring is "12233" and its digit sum is \(1+2+2+3+3=11\).

Note: When k reaches 10 or above, the number is multi-digit; however, the construction rule still applies: append k copies of the string representation of k. For example, for k=10, append "10" 10 times.

inputFormat

The input consists of two space-separated integers: l and r, where 1 ≤ l ≤ r, representing the positions in the string (1-indexed).

outputFormat

Output a single integer which is the sum of the digits in the substring from the l-th to the r-th position.

sample

1 5

11