Cascade Amplifier Compressed Gain

A signal-processing test bench chains together amplifiers labeled with every integer from L to R, inclusive. The amplifier labeled k multiplies the amplitude of the signal passing through it by exactly k, so the bench's total gain G equals the product of every integer from L to R.

Because the bench's numeric display is narrow, G is never shown as a raw decimal integer. Instead the display renders G's compressed form, built as follows:

1. Write G in base 10 (it never has leading zeros, since G is always a positive integer).
2. Strip every trailing zero digit from G. Call the number of digits stripped e, and call the remaining digit string core (core is never empty).
3. Let d be the number of digits in core.
4. If d is at most 10, the compressed form is core followed by the letter e followed by the decimal value of e (no leading zeros).
5. If d is greater than 10, the compressed form is the first 5 digits of core, followed by the three characters ..., followed by the last 5 digits of core, followed by the letter e followed by the decimal value of e.

Given L and R, print the bench's total gain in compressed form.

Input format

A single line containing two integers L and R, separated by a single space.

Output format

A single line containing the compressed form of G, exactly as described above, with no surrounding whitespace.

Constraints

1 <= L <= R <= 2000

1 4

24e0

2 11

399168e2