A9057. Parity Game

You are fishing with polar bears Alice and Bob. While waiting for the fish to bite, the polar bears get bored. They come up with a game. First Alice and Bob each writes a 01-string (strings that only contain character "0" and "1") $a$ and $b$ . Then you try to turn $a$ into $b$ using two types of operations:

- Write $parity(a)$ to the end of $a$ . For example, .
- Remove the first character of $a$ . For example, . You cannot perform this operation if $a$ is empty.

You can use as many operations as you want. The problem is, is it possible to turn $a$ into $b$ ?

The $parity$ of a 01-string is $1$ if there is an odd number of "1"s in the string, and $0$ otherwise.

The first line contains the string $a$ and the second line contains the string $b$ $(1<=|a|,|b|<=1000)$ . Both strings contain only the characters "0" and "1". Here $|x|$ denotes the length of the string $x$ .

Print "YES" (without quotes) if it is possible to turn $a$ into $b$ , and "NO" (without quotes) otherwise.

In the first sample, the steps are as follows: $01011→1011→011→0110$