# Concatenation of Consecutive Binary Numbers

Given an integer n, return the decimal value of the binary string formed by concatenating the binary representations of 1 to n in order, modulo 109 + 7.

Example 1:

```Input: n = 1
Output: 1
Explanation: "1" in binary corresponds to the decimal value 1.
```
Example 2:

```Input: n = 3
Output: 27
Explanation: In binary, 1, 2, and 3 corresponds to "1", "10", and "11".
After concatenating them, we have "11011", which corresponds to the decimal value 27.
```
Example 3:

```Input: n = 12
Output: 505379714
Explanation: The concatenation results in "1101110010111011110001001101010111100".
The decimal value of that is 118505380540.
After modulo 109 + 7, the result is 505379714.
```

Constraints:

• 1 <= n <= 105

Solution:

```class Solution {
int mod = (int) 1e9 + 7;

public int concatenatedBinary(int n) {
// f(0) = 0
// f(1) = f(0) << 0 + 1 = 1
// f(2) = f(1) << 2 + 2 = 6
// f(3) = f(2) << 2 + 3 = 27
long res = 0;
for (int i = 1; i <= n; ++i) {
int len = 0;
for (int j = i; j > 0; j >>= 1, ++len);
res = ((res << len) % mod + i) % mod;
// System.out.println(res);
}
return (int) (res % mod);
}
}```