Problem:
Score: 200 points

Problem Statement

M-kun has the following three cards:

A red card with the integer A.

A green card with the integer B.

A blue card with the integer C.

He is a genius magician who can do the following operation at most K times:

Choose one of the three cards and multiply the written integer by 2.

His magic is successful if both of the following conditions are satisfied after the operations:

The integer on the green card is strictly greater than the integer on the red card.

The integer on the blue card is strictly greater than the integer on the green card.

Determine whether the magic can be successful.

Constraints

1 \leq A, B, C \leq 7

1 \leq K \leq 7

All values in input are integers.

Input

Input is given from Standard Input in the following format:

A B C
K

Output

If the magic can be successful, print Yes; otherwise, print No.

Sample Input 1

7 2 5
3

Sample Output 1

Yes

The magic will be successful if, for example, he does the following operations:

First, choose the blue card. The integers on the red, green, and blue cards are now 7, 2, and 10, respectively.

Second, choose the green card. The integers on the red, green, and blue cards are now 7, 4, and 10, respectively.

Third, choose the green card. The integers on the red, green, and blue cards are now 7, 8, and 10, respectively.

Sample Input 2

7 4 2
3

Sample Output 2

No

He has no way to succeed in the magic with at most three operations.

Solution in Rust (1.42.0) (judge verdict: Accepted)

#![allow(unused_imports)]

// language: Rust(1.42.0)
// check available crates on AtCoder at "https://atcoder.jp/contests/language-test-202001"
// My Library Repositry is at "https://github.com/Loptall/sfcpl"

/*
    青perfほしいよ〜！
*/

// from std...
use std::cmp::{
    max, min, Ordering,
    Ordering::{Equal, Greater, Less},
    Reverse,
};
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
use std::convert::TryInto;
use std::fmt;
use std::mem::swap;
use std::num::{NonZeroU32, ParseIntError};
use std::ops::{
    Add, AddAssign, BitAnd, BitAndAssign, BitOr, BitOrAssign, BitXor, BitXorAssign, Div, DivAssign,
    Index, IndexMut, Mul, MulAssign, Neg, Rem, RemAssign, Shl, ShlAssign, Shr, ShrAssign, Sub,
    SubAssign,
};
use std::process::exit;
use std::{f32, f64, i128, i16, i32, i64, i8, isize, u128, u16, u32, u64, u8, usize};

// Dep' crates are...
use itertools::*;
use itertools_num::*;
use lazy_static::lazy_static;
use maplit::{btreemap, btreeset, hashmap, hashset};
use num_bigint::{BigInt, BigUint};
use num_complex::Complex;
use num_integer::{binomial, gcd, lcm, multinomial, Integer};
use num_rational::Rational;
use num_traits::{
    clamp, one, pow, zero, Num, NumAssignOps, NumOps, One, Pow, Signed, Unsigned, Zero,
};
use permutohedron::Heap;
use proconio::{
    derive_readable, fastout, input, is_stdin_empty,
    marker::{Bytes, Chars, Isize1, Usize1},
};
use rand::random;

pub trait Visualize {
    fn visualize(&self, split: &str);
    fn continuous(&self) {
        self.visualize("");
    }
    fn spaces(&self) {
        self.visualize(" ");
    }
    fn lines(&self) {
        self.visualize("\n");
    }
}
macro_rules! impl_vis_for_sized {
    ($($t:ty),+) => {
        $(
            impl Visualize for $t {
                fn visualize(&self, _split: &str) {
                    print!("{}", self);
                }
            }
        )+
    };
}
impl_vis_for_sized! {
    usize, u8, u16, u32, u64, u128,
    isize, i8, i16, i32, i64, i128,
    f64, f32,
    String, &str, char
}
impl<T: fmt::Display> Visualize for [T] {
    fn visualize(&self, split: &str) {
        print!("{}", self.iter().join(split));
    }
}
#[macro_export]
macro_rules! vis {
    // end
    () => {
        println!();
    };

    // last element + trailing pattern
    ($last:expr ;) => {
        $last.lines();
        vis!()
    };
    ($last:expr =>) => {
        $last.continuous();
        vis!();
    };
    ($last:expr $(,)?) => {
        $last.spaces();
        vis!();
    };

    // get first element and pass rest
    ($first:expr; $($rest:tt)*) => {
        $first.lines();
        println!();
        vis!($($rest)*);
    };
    ($first:expr => $($rest:tt)*) => {
        $first.continuous();
        vis!($($rest)*);
    };
    ($first:expr, $($rest:tt)*) => {
        $first.spaces();
        print!(" ");
        vis!($($rest)*);
    };
}
pub const MOD10E9_7: usize = 1000000007; // 10 ^ 9 + 7
pub const MOD99_: usize = 998244353;
pub const MAX: usize = std::usize::MAX; // = 2 ^ 64 - 1 = 18446744073709551615 ≈ 1.8 * 10 ^ 19
pub const INF: usize = 2000000000000000000; // MAX / 9 < 2 * 10e18 < MAX / 10
pub const FNI: i64 = -2000000000000000000; // == -(INF as i64)
pub const PI: f64 = f64::consts::PI; // 3.141592653589793 -- 10 ^ -15
pub const ASCII_A_LARGE: u8 = 65;
pub const ASCII_A_SMALL: u8 = 97;
pub const ASCII_0: u8 = 48;
pub const ADJ4: &[(isize, isize); 4] = &[(1, 0), (0, 1), (-1, 0), (0, -1)];
pub const ADJ8: &[(isize, isize); 8] = &[
    (1, 0),
    (1, 1),
    (0, 1),
    (-1, 1),
    (-1, 0),
    (-1, -1),
    (0, -1),
    (1, -1),
];

// code...
// #[fastout]
fn main() {
    input! {
        a: usize, b: usize, c: usize,
        k: usize
    }

    for i in 0..=k {
        for j in 0..=(k-i) {
            let l = k - i - j;
            dbg!(i, j, l);
            let a = a * 2usize.pow(i as u32);
            let b = b * 2usize.pow(j as u32);
            let c = c * 2usize.pow(l as u32);
            if a < b && b < c {
                vis!("Yes");
                return;
            }
        }
    }

    vis!("No");
}