You are given a decimal string ~s~ and an integer ~k~.

Delete exactly ~k~ digits from ~s~ so that the remaining digits, in their original order, form the smallest possible number.

If the resulting number has leading zeroes, do not print them. If every digit is deleted, or the result is all zeroes, print 0.

Input

The first line contains the string ~s~.

The second line contains the integer ~k~.

Output

Print the smallest possible number after deleting exactly ~k~ digits.

Constraints

• ~1 \le |s| \le 2 \cdot 10^5~
• ~0 \le k \le |s|~
• ~s~ consists only of digits 0 through 9

Example 1

Input

1432219
3

Output

1219

Explanation

Deleting the digits 4, 3, and 2 gives the smallest possible result.

Example 2

Input

10200
1

Output

200

Explanation

Deleting the leading 1 gives 0200, which is printed as 200.

Example 3

Input

10
2

Output

0