## 1201. Ugly Number III

Given four integers `n`

, `a`

, `b`

, and `c`

, return the `n`

ugly number.^{th}

Ugly numbers are **positive integers** that are divisible by `a`

, `b`

, or `c`

.

**Example 1:**

Input:n = 3, a = 2, b = 3, c = 5Output:4Explanation:The ugly numbers are 2, 3, 4, 5, 6, 8, 9, 10... The 3rd is 4.

**Example 2:**

Input:n = 4, a = 2, b = 3, c = 4Output:6Explanation:The ugly numbers are 2, 3, 4, 6, 8, 9, 10, 12... The 4th is 6.

**Example 3:**

Input:n = 5, a = 2, b = 11, c = 13Output:10Explanation:The ugly numbers are 2, 4, 6, 8, 10, 11, 12, 13... The 5th is 10.

**Example 4:**

Input:n = 1000000000, a = 2, b = 217983653, c = 336916467Output:1999999984

**Constraints:**

`1 <= n, a, b, c <= 10`

^{9}`1 <= a * b * c <= 10`

^{18}- It is guaranteed that the result will be in range
`[1, 2 * 10`

.^{9}]

## Rust Solution

```
struct Solution;
impl Solution {
fn nth_ugly_number(n: i32, a: i32, b: i32, c: i32) -> i32 {
let mut left = 0;
let mut right = 2_000_000_000;
while left < right {
let mid = left + (right - left) / 2;
if Self::count(mid, a as u64, b as u64, c as u64) < n as u64 {
left = mid + 1;
} else {
right = mid
}
}
left as i32
}
fn count(num: u64, a: u64, b: u64, c: u64) -> u64 {
num / a + num / b + num / c
- num / Self::lcm(a, b)
- num / Self::lcm(b, c)
- num / Self::lcm(a, c)
+ num / Self::lcm(a, Self::lcm(b, c))
}
fn lcm(a: u64, b: u64) -> u64 {
a * b / Self::gcd(a, b)
}
fn gcd(a: u64, b: u64) -> u64 {
if a == 0 {
b
} else {
Self::gcd(b % a, a)
}
}
}
#[test]
fn test() {
let n = 3;
let a = 2;
let b = 3;
let c = 5;
let res = 4;
assert_eq!(Solution::nth_ugly_number(n, a, b, c), res);
let n = 4;
let a = 2;
let b = 3;
let c = 4;
let res = 6;
assert_eq!(Solution::nth_ugly_number(n, a, b, c), res);
let n = 5;
let a = 2;
let b = 11;
let c = 13;
let res = 10;
assert_eq!(Solution::nth_ugly_number(n, a, b, c), res);
let n = 1000000000;
let a = 2;
let b = 217983653;
let c = 336916467;
let res = 1999999984;
assert_eq!(Solution::nth_ugly_number(n, a, b, c), res);
}
```

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