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.

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.)