## 1680. 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`

## Rust Solution

``````struct Solution;

const MOD: i64 = 1_000_000_007;

impl Solution {
fn concatenated_binary(n: i32) -> i32 {
let mut res = 0;
let mut stack: Vec<i64> = vec![];
for i in 1..=n {
let mut j = i;
while j > 0 {
stack.push((j % 2) as i64);
j >>= 1;
}
while let Some(top) = stack.pop() {
res <<= 1;
res += top;
}
res %= MOD;
}
res as i32
}
}

#[test]
fn test() {
let n = 1;
let res = 1;
assert_eq!(Solution::concatenated_binary(n), res);
let n = 3;
let res = 27;
assert_eq!(Solution::concatenated_binary(n), res);
let n = 12;
let res = 505379714;
assert_eq!(Solution::concatenated_binary(n), res);
}
``````

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