200593: [AtCoder]ARC059 F - Unhappy Hacking

Memory Limit:256 MB Time Limit:2 S
Judge Style:Text Compare Creator:
Submit:0 Solved:0

Description

Score : $800$ points

Problem Statement

Sig has built his own keyboard. Designed for ultimate simplicity, this keyboard only has $3$ keys on it: the 0 key, the 1 key and the backspace key.

To begin with, he is using a plain text editor with this keyboard. This editor always displays one string (possibly empty). Just after the editor is launched, this string is empty. When each key on the keyboard is pressed, the following changes occur to the string:

  • The 0 key: a letter 0 will be inserted to the right of the string.
  • The 1 key: a letter 1 will be inserted to the right of the string.
  • The backspace key: if the string is empty, nothing happens. Otherwise, the rightmost letter of the string is deleted.

Sig has launched the editor, and pressed these keys $N$ times in total. As a result, the editor displays a string $s$. Find the number of such ways to press the keys, modulo $10^9 + 7$.

Constraints

  • $1 ≦ N ≦ 5000$
  • $1 ≦ |s| ≦ N$
  • $s$ consists of the letters 0 and 1.

Partial Score

  • $400$ points will be awarded for passing the test set satisfying $1 ≦ N ≦ 300$.

Input

The input is given from Standard Input in the following format:

$N$
$s$

Output

Print the number of the ways to press the keys $N$ times in total such that the editor displays the string $s$ in the end, modulo $10^9+7$.


Sample Input 1

3
0

Sample Output 1

5

We will denote the backspace key by B. The following $5$ ways to press the keys will cause the editor to display the string 0 in the end: 00B, 01B, 0B0, 1B0, BB0. In the last way, nothing will happen when the backspace key is pressed.


Sample Input 2

300
1100100

Sample Output 2

519054663

Sample Input 3

5000
01000001011101000100001101101111011001000110010101110010000

Sample Output 3

500886057

Input

题意翻译

小z得到了一个键盘,里面只有$1, 0$和退格键 键$0$可以打出一个$0$的字符串,键$1$同理 退格键可以删除前面打出的那个字符 小z可以操作这个键盘$N$次($N\le5000$),求操作完成后打出来的字符串恰好是$S$的方案数 注意:当前没有字符也可以使用退格键

加入题单

上一题 下一题 算法标签: