[ABC129E] Sum Equals Xor

ID: 17996

传统题

2000ms

1024MiB

难度: 4

上传者:

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?

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

What is XOR?

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

When $A \text{ XOR } B$ 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, $3 \text{ XOR } 5 = 6$ . (In base two: $011 \text{ XOR } 101 = 110$ .)

Input is given from Standard Input in the following format:

$L$

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

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

1111111111111111111

162261460