Problem:
Score : 200 points

Problem Statement

We ask you to select some number of positive integers, and calculate the sum of them.

It is allowed to select as many integers as you like, and as large integers as you wish.
You have to follow these, however: each selected integer needs to be a multiple of A, and you need to select at least one integer.

Your objective is to make the sum congruent to C modulo B.
Determine whether this is possible.

If the objective is achievable, print YES. Otherwise, print NO.

Constraints

1 ≤ A ≤ 100

1 ≤ B ≤ 100

0 ≤ C < B

Input

Input is given from Standard Input in the following format:

A B C

Output

Print YES or NO.

Sample Input 1

7 5 1

Sample Output 1

YES

For example, if you select 7 and 14, the sum 21 is congruent to 1 modulo 5.

Sample Input 2

2 2 1

Sample Output 2

NO

The sum of even numbers, no matter how many, is never odd.

Sample Input 3

1 100 97

Sample Output 3

YES

You can select 97, since you may select multiples of 1, that is, all integers.

Sample Input 4

40 98 58

Sample Output 4

YES

Sample Input 5

77 42 36

Sample Output 5

NO

Solution in Rust (1.15.1) (judge verdict: Accepted)

use std::cmp;
use std::collections::HashSet;

macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };

    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };

    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };

    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };

    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

#[inline]
pub fn clamp<T: PartialOrd>(input: T, min: T, max: T) -> T {
    debug_assert!(min <= max, "min must be less than or equal to max");
    if input < min {
        min
    } else if input > max {
        max
    } else {
        input
    }
}

#[allow(dead_code)]
fn practice_1() {
    input! {
    n: i32,
    m: [i32; 2],
    s: chars,
    }
    let s: Vec<char> = s;
    let s: String = s.into_iter().collect();

    println!("{} {}", n + m[0] + m[1], s);
}

#[allow(dead_code)]
fn abc086_a() {
    input! {
    n: [i32; 2],
    }
    let prod: i32 = n[0] * n[1];
    let res = if prod % 2 == 0 {
        "Even"
    } else {
        "Odd"
    };
    println!("{}", res)
}

#[allow(dead_code)]
fn abc081_a() {
    input! {
    s: chars,
    }
    let s: Vec<char> = s;
    let res: u32 = s.iter().map(|n| n.to_digit(10).unwrap()).sum();

    println!("{}", res)
}

#[allow(dead_code)]
fn abc081_b() {
    input! {
    n: i32,
    arr: [i32; n],
    }
    let mut arr: Vec<i32> = arr;
    let mut cnt = 0;

    loop {
        if arr.iter().any(|v| (v % 2) == 1) {
            break;
        }
        arr = arr.iter().map(|v| v / 2).collect();
        cnt += 1;
    }

    println!("{}", cnt)
}

#[allow(dead_code)]
fn abc083_b() {
    input! {
    arr: [i32; 3],
    }

    let n: i32 = arr[0];
    let a: i32 = arr[1];
    let b: i32 = arr[2];

    let (vals, _total): (Vec<i32>, Vec<i32>) = (0..n + 1)
        .map(|i| {
            let d0 = i - (i / 10) * 10;
            let d1 = (i / 10) - (i / 100) * 10;
            let d2 = (i / 100) - (i / 1000) * 10;
            let d3 = (i / 1000) - (i / 10000) * 10;
            let d4 = (i / 10000) - (i / 100000) * 10;
            (i, d0 + d1 + d2 + d3 + d4)
        })
        .filter(|&(_i, total)| {
            (a <= total) && (total <= b)
        })
        .unzip();
//        .for_each(|(i, _total)| {
//            res += i;
//        });
    let res: i32 = vals.iter().sum();

    println!("{:?}", res)
}

#[allow(dead_code)]
fn abc087_b() {
    input! {
    n_500: i32,
    n_100: i32,
    n_50: i32,
    total: i32,
    }

    let n_500: i32 = n_500;
    let n_100: i32 = n_100;
    let n_50: i32 = n_50;
    let total: i32 = total;
    let mut cnt = 0;

    for i in 0..n_500 + 1 {
        for j in 0..n_100 + 1 {
            for k in 0..n_50 + 1 {
                let total_tried = i * 500 + j * 100 + k * 50;
                if total_tried == total {
//                    println!("{}, {}, {}", i, j, k);
                    cnt += 1;
                }
            }
        }
    }

    println!("{}", cnt)
}

#[allow(dead_code)]
fn abc088_b() {
    input! {
    n_items: i32,
    arr: [i32; n_items],
    }

    let mut arr: Vec<i32> = arr;
    arr.sort();

    let res: i32 = arr.iter().rev()
        .enumerate()
        .map(|(i, &v)| {
            if (i % 2) == 0 {
                v
            } else {
                -v
            }
        })
        .sum();

    println!("{:?}", res)
}

#[allow(dead_code)]
fn abc085_b() {
    input! {
    n_: usize,
    arr: [[i32; 1]; n_],
    }

    let arr: Vec<Vec<i32>> = arr;
    let res = arr.iter()
//        .flatten()
        .flat_map(|a| a)
        .cloned()
        .collect::<HashSet<i32>>()
        .len();

    println!("{:?}", res)
}

#[allow(dead_code)]
fn abc085_c() {
    input! {
    args: [u32; 2],
    }

    let n: u32 = args[0];
    let total: u32 = args[1];

    let x_max = cmp::min(total / 10_000, n) + 1;

    for x in (0..x_max).rev() {
        if x * 10_000 > total { break; }
        let y_max = cmp::min(total / 5_000, n - x) + 1;
        for y in (0..y_max).rev() {
            let z = n - x - y;
            if x * 10_000 + y * 5_000 + z * 1_000 == total {
                println!("{} {} {}", x, y, z);
                return;
            }
        }
    }

    println!("-1 -1 -1")
}


#[allow(dead_code)]
fn arc065_a() {
    input! {
    arr: chars,
    }
    let mut arr: Vec<char> = arr;

    let dream: Vec<char> = "dream".chars().collect();
    let dreamer: Vec<char> = "dreamer".chars().collect();
    let erase: Vec<char> = "erase".chars().collect();
    let eraser: Vec<char> = "eraser".chars().collect();

    fn rel(n: i32) -> i32 {
        if n < 0 {
            0
        } else {
            n
        }
    }

    loop {
        let size = arr.len() as i32;
        if size == 0 {
            println!("YES");
            return;
        }

        let last_5 = rel(size - 5) as usize;
        let last_6 = rel(size - 6) as usize;
        let last_7 = rel(size - 7) as usize;

        let is_dream = arr[last_5..].to_vec() == dream;
        let is_dreamer = arr[last_7..].to_vec() == dreamer;
        let is_erase = arr[last_5..].to_vec() == erase;
        let is_eraser = arr[last_6..].to_vec() == eraser;

        if is_dream {
            arr.drain(last_5..);
        } else if is_dreamer {
            arr.drain(last_7..);
        } else if is_erase {
            arr.drain(last_5..);
        } else if is_eraser {
            arr.drain(last_6..);
        } else {
            println!("NO");
            return;
        }
    }
}

#[allow(dead_code)]
fn arc089_a() {
    input! {
    n_: usize,
    arr: [[u32; 3]; n_],
    }

    let arr: Vec<Vec<u32>> = arr;

    for a in arr {
        let t = a[0];
        let x = a[1];
        let y = a[2];

        // Check dist
        if x + y > t {
            println!("No");
            return;
        }

        if ((x + y) % 2) == 0 && (t % 2) == 0 {
            continue;
        }

        if ((x + y) % 2) == 1 && (t % 2) == 1 {
            continue;
        }

        println!("No");
        return;
    }

    println!("Yes");
}

#[allow(dead_code)]
fn abc075_b() {
    input! {
        h: i32,
        w: i32,
        board: [chars; h],
    }
    let board: Vec<Vec<char>> = board;

    for r in 0..h {
        for c in 0..w {
//            println!("{} {}", r, c);
            if board[r as usize][c as usize] == '#' {
                print!("#");
                continue;
            }

            let r_min = clamp(r - 1, 0, h) as usize;
            let r_max = clamp(r + 2, 0, h) as usize;
            let c_min = clamp(c - 1, 0, w) as usize;
            let c_max = clamp(c + 2, 0, w) as usize;

            let mut total = 0;

            for r_tmp in r_min..r_max {
                for c_tmp in c_min..c_max {
                    let val = board[r_tmp][c_tmp];
//                    println!("{} {} {} {} {}", val, r_min, r_max, c_min, c_max);
                    if val == '#' {
                        total += 1;
                    }
                }
            }
            print!("{}", total);
        }
        println!("");
    }
}

#[allow(dead_code)]
fn abc096_c() {
    input! {
        h: i32,
        w: i32,
        board: [chars; h],
    }
    let board: Vec<Vec<char>> = board;

    for r in 0..h {
        for c in 0..w {
            if board[r as usize][c as usize] == '.' {
                continue;
            }

            let r_min = clamp(r - 1, 0, h) as usize;
            let r_max = clamp(r + 2, 0, h) as usize;
            let c_min = clamp(c - 1, 0, w) as usize;
            let c_max = clamp(c + 2, 0, w) as usize;

            let mut has_neighbour = false;

            for r_tmp in r_min..r_max {
                for c_tmp in c_min..c_max {
                    if r_tmp == r as usize && c_tmp == c as usize {
                        continue;
                    }
                    if r_tmp != r as usize && c_tmp != c as usize {
                        continue;
                    }
                    let val = board[r_tmp][c_tmp];
                    if val == '#' {
                        has_neighbour = true;
                        break;
                    }
                }
            }

            if !has_neighbour {
                print!("No");
                return;
            }
        }
    }
    print!("Yes");
}

#[allow(dead_code)]
fn abc070_b() {
    input! {
        a0: u32,
        a1: u32,
        b0: u32,
        b1: u32,
    }
    let a: HashSet<u32> = (a0..a1).collect();
    let b: HashSet<u32> = (b0..b1).collect();
    let res = a.intersection(&b)
        .cloned()
        .collect::<HashSet<u32>>()
        .len();
    println!("{}", res);
}

#[allow(dead_code)]
fn abc055_b() {
    input! {
        n: u64,
    }
    let res = (1..n + 1)
        .fold(1, |acc, x| {
            (acc * x) % (1e+9 as u64 + 7)
        });
    println!("{}", res);
}

#[allow(dead_code)]
fn abc046_b() {
    input! {
        n: u32,
        m: u32,
    }
    let res = (1..n)
        .fold(m, |acc, _x| acc * (m - 1));
    println!("{}", res);
}

#[allow(dead_code)]
fn abc048_b() {
    input! {
        a: i64,
        b: i64,
        x: i64,
    }
    fn f(n: i64, x: i64) -> i64 {
        if n >= 0 {
            n / x + 1
        } else {
            0
        }
    }
    let res = f(b, x) - f(a - 1, x);
    println!("{}", res);
}

#[allow(dead_code)]
fn abc060_b() {
    input! {
        a: i32,
        b: i32,
        c: i32,
    }
    let res = (1..(b + 1))
        .map(|n| (a * n) % b == c)
        .any(|x| x);

    if res {
        println!("YES");
    } else {
        println!("NO");
    }
}

fn main() {
    abc060_b()
}