use vstd::prelude::*;

fn main() {}

verus! {

pub struct Solution;

impl Solution {
    pub closed spec fn is_sequential_digits(n: int) -> bool
        decreases n
    {
        if n < 10 {
            1 <= n && n <= 9
        } else {
            let last = n % 10;
            let rest = n / 10;
            let prev = rest % 10;
            2 <= last && last <= 9 && prev == last - 1 && Self::is_sequential_digits(rest)
        }
    }

    pub fn sequential_digits(low: i32, high: i32) -> (result: Vec<i32>)
        requires
            10 <= low <= high <= 1000000000,
        ensures
            forall|i: int| 0 <= i < result.len() ==> low <= #[trigger] result[i] <= high,
            forall|i: int| 0 <= i < result.len() ==> Self::is_sequential_digits(#[trigger] result[i] as int),
            forall|i: int, j: int| 0 <= i < j < result.len() ==> #[trigger] result[i] < #[trigger] result[j],
            forall|x: int| (low <= x <= high && Self::is_sequential_digits(x)) ==> exists|k: int| 0 <= k < result.len() && #[trigger] result[k] == x as i32,
    {
        let candidates = [
            12i32, 23, 34, 45, 56, 67, 78, 89,
            123, 234, 345, 456, 567, 678, 789,
            1234, 2345, 3456, 4567, 5678, 6789,
            12345, 23456, 34567, 45678, 56789,
            123456, 234567, 345678, 456789,
            1234567, 2345678, 3456789,
            12345678, 23456789,
            123456789,
        ];

        let mut result: Vec<i32> = Vec::new();
        let mut i = 0;
        while i < candidates.len()
        {
            let x = candidates[i];
            if low <= x && x <= high {
                result.push(x);
            }
            i += 1;
        }
        result
    }
}

}