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Contest: Task: Related: TaskD TaskF

Score : $500$ points

Problem Statement

You are given a positive integer $L$ in base two. How many pairs of non-negative integers $(a, b)$ satisfy the following conditions?

  • $a + b \leq L$
  • $a + b = a \mbox{ XOR } b$

Since there can be extremely many such pairs, print the count modulo $10^9 + 7$.

What is XOR?

The XOR of integers $A$ and $B$, $A \mbox{ XOR } B$, is defined as follows:

  • When $A \mbox{ XOR } B$ is written in base two, the digit in the $2^k$'s place ($k \geq 0$) is $1$ if either $A$ or $B$, but not both, has $1$ in the $2^k$'s place, and $0$ otherwise.

For example, $3 \mbox{ XOR } 5 = 6$. (In base two: $011 \mbox{ XOR } 101 = 110$.)

Constraints

  • $L$ is given in base two, without leading zeros.
  • $1 \leq L < 2^{100\ 001}$

Input

Input is given from Standard Input in the following format:

$L$

Output

Print the number of pairs $(a, b)$ that satisfy the conditions, modulo $10^9 + 7$.

Sample Input 1

10

Sample Output 1

5

Five pairs $(a, b)$ satisfy the conditions: $(0, 0), (0, 1), (1, 0), (0, 2)$ and $(2, 0)$.

Sample Input 2

1111111111111111111

Sample Output 2

162261460