Consider two n-digit positive decimal integers A and B with no leading
zeroes. We need to find the two closest to A n-digit numbers (the
first one – greater or equal to A, the other – strictly less than A),
with decimal writings containing all the digits of B in some order.
For example if A=3022 and B=1232, using B’s digits we can obtain
the following 4-digit numbers: 1223, 1232, 1322, 2123, 2132, 2213,
2231, 2312, 2321, 3122, 3212 and 3221. The least number greater
or equal to A obtained by B’s digits is 3122, and the biggest one,
strictly less then A is 2321. If A=1232 and B=3022, the possible numbers
are 2023, 2032, 2203, 2230, 2302, 2320, 3022, 3202 and
3220. The least number greater or equal to A obtained by B’s digits
is 2023, and there is no number less than A.
Write a program closest to find these “closest to A” numbers for
given A and B, or to determine that one of them does not exist.
INPUT
Two lines are read from the standard input, each of them containing an
n-digit positive integer with no leading zeroes, with A read from the
first, and B read from the second line (1≤n ≤ 60).
SAMPLE INPUT
Example 1 Example 2
3075 3000203
6604 4562454
OUTPUT
Write to the standard output:
- Line 1: the least n-digit number with no leading zeroes,
not less than A, containing all the digits of B in some order.
If such number does not exist, the output should be 0.
- Line 2: the biggest n-digit number with no leading zeroes, less
than A, containing all the digits of B in some order. If such number
does not exist, the output should be 0.
SAMPLE OUTPUT
Example 1 Example 2
4066 4244556
0 2655444
Problem for kid - Please, think like kid.