Problem:
Score : 300 points

Problem Statement

Tak has N cards. On the i-th (1 \leq i \leq N) card is written an integer x_i.
He is selecting one or more cards from these N cards, so that the average of the integers written on the selected cards is exactly A.
In how many ways can he make his selection?

Constraints

1 \leq N \leq 50

1 \leq A \leq 50

1 \leq x_i \leq 50

N,\,A,\,x_i are integers.

Partial Score

200 points will be awarded for passing the test set satisfying 1 \leq N \leq 16.

Input

The input is given from Standard Input in the following format:

N A
x_1 x_2 ... x_N

Output

Print the number of ways to select cards such that the average of the written integers is exactly A.

Sample Input 1

4 8
7 9 8 9

Sample Output 1

5

The following are the 5 ways to select cards such that the average is 8:

Select the 3-rd card.

Select the 1-st and 2-nd cards.

Select the 1-st and 4-th cards.

Select the 1-st, 2-nd and 3-rd cards.

Select the 1-st, 3-rd and 4-th cards.

Sample Input 2

3 8
6 6 9

Sample Output 2

0

Sample Input 3

8 5
3 6 2 8 7 6 5 9

Sample Output 3

19

Sample Input 4

33 3
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

Sample Output 4

8589934591

The answer may not fit into a 32-bit integer.

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

use std::cmp;
use std::cmp::{max, min};
use std::cmp::Ordering::{self, Greater, Less};
use std::collections::{HashMap, HashSet};
use std::f64::consts::PI;

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")
    };
}

pub trait Ext {
    type Item;

    fn lower_bound(&self, x: &Self::Item) -> usize
        where
            Self::Item: Ord;

    fn lower_bound_by<'a, F>(&'a self, f: F) -> usize
        where
            F: FnMut(&'a Self::Item) -> Ordering;

    fn lower_bound_by_key<'a, K, F>(&'a self, k: &K, f: F) -> usize
        where
            F: FnMut(&'a Self::Item) -> K,
            K: Ord;

    fn upper_bound(&self, x: &Self::Item) -> usize
        where
            Self::Item: Ord;

    fn upper_bound_by<'a, F>(&'a self, f: F) -> usize
        where
            F: FnMut(&'a Self::Item) -> Ordering;

    fn upper_bound_by_key<'a, K, F>(&'a self, k: &K, f: F) -> usize
        where
            F: FnMut(&'a Self::Item) -> K,
            K: Ord;

    fn equal_range(&self, x: &Self::Item) -> std::ops::Range<usize>
        where
            Self::Item: Ord;

    fn equal_range_by<'a, F>(&'a self, f: F) -> std::ops::Range<usize>
        where
            F: FnMut(&'a Self::Item) -> Ordering;

    fn equal_range_by_key<'a, K, F>(&'a self, k: &K, f: F) -> std::ops::Range<usize>
        where
            F: FnMut(&'a Self::Item) -> K,
            K: Ord;
}

impl<T> Ext for [T] {
    type Item = T;

    fn lower_bound(&self, x: &Self::Item) -> usize
        where
            T: Ord,
    {
        self.lower_bound_by(|y| y.cmp(x))
    }
    fn lower_bound_by<'a, F>(&'a self, mut f: F) -> usize
        where
            F: FnMut(&'a Self::Item) -> Ordering,
    {
        let s = self;
        let mut size = s.len();
        if size == 0 {
            return 0;
        }
        let mut base = 0usize;
        while size > 1 {
            let half = size / 2;
            let mid = base + half;
            let cmp = f(unsafe { s.get_unchecked(mid) });
            base = if cmp == Less { mid } else { base };
            size -= half;
        }
        let cmp = f(unsafe { s.get_unchecked(base) });
        base + (cmp == Less) as usize
    }
    fn lower_bound_by_key<'a, K, F>(&'a self, k: &K, mut f: F) -> usize
        where
            F: FnMut(&'a Self::Item) -> K,
            K: Ord,
    {
        self.lower_bound_by(|e| f(e).cmp(k))
    }

    fn upper_bound(&self, x: &Self::Item) -> usize
        where
            T: Ord,
    {
        self.upper_bound_by(|y| y.cmp(x))
    }

    fn upper_bound_by<'a, F>(&'a self, mut f: F) -> usize
        where
            F: FnMut(&'a Self::Item) -> Ordering,
    {
        let s = self;
        let mut size = s.len();
        if size == 0 {
            return 0;
        }
        let mut base = 0usize;
        while size > 1 {
            let half = size / 2;
            let mid = base + half;
            let cmp = f(unsafe { s.get_unchecked(mid) });
            base = if cmp == Greater { base } else { mid };
            size -= half;
        }
        let cmp = f(unsafe { s.get_unchecked(base) });
        base + (cmp != Greater) as usize
    }
    fn upper_bound_by_key<'a, K, F>(&'a self, k: &K, mut f: F) -> usize
        where
            F: FnMut(&'a Self::Item) -> K,
            K: Ord,
    {
        self.upper_bound_by(|e| f(e).cmp(k))
    }

    fn equal_range(&self, x: &Self::Item) -> std::ops::Range<usize>
        where
            T: Ord,
    {
        self.equal_range_by(|y| y.cmp(x))
    }
    fn equal_range_by<'a, F>(&'a self, mut f: F) -> std::ops::Range<usize>
        where
            F: FnMut(&'a Self::Item) -> Ordering,
    {
        let s = self;
        let mut size = s.len();
        if size == 0 {
            return 0..0;
        }
        let mut base = (0usize, 0usize);
        while size > 1 {
            let half = size / 2;
            let mid = (base.0 + half, base.1 + half);
            let cmp = (
                f(unsafe { s.get_unchecked(mid.0) }),
                f(unsafe { s.get_unchecked(mid.1) }),
            );
            base = (
                if cmp.0 == Less { mid.0 } else { base.0 },
                if cmp.1 == Greater { base.1 } else { mid.1 },
            );
            size -= half;
        }
        let cmp = (
            f(unsafe { s.get_unchecked(base.0) }),
            f(unsafe { s.get_unchecked(base.1) }),
        );
        (base.0 + (cmp.0 == Less) as usize..base.1 + (cmp.1 != Greater) as usize)
    }

    fn equal_range_by_key<'a, K, F>(&'a self, k: &K, mut f: F) -> std::ops::Range<usize>
        where
            F: FnMut(&'a Self::Item) -> K,
            K: Ord,
    {
        self.equal_range_by(|e| f(e).cmp(k))
    }
}

pub struct UnionFind {
    parts: Vec<usize>
}

impl UnionFind {
    pub fn new(n: usize) -> UnionFind {
        let parts = (0..n).collect();
        UnionFind { parts: parts }
    }

    pub fn union(&mut self, i: usize, j: usize) {
        let i_leader = self.find(i);
        let j_leader = self.find(j);
        self.parts[j_leader] = self.parts[i_leader];
    }

    pub fn find(&mut self, i: usize) -> usize {
        let mut p = i;
        while self.parts[p] != p {
            p = self.parts[p]
        };
        let mut s = i;
        while s != p {
            let t = self.parts[s];
            self.parts[s] = p;
            s = t
        };
        p
    }

    pub fn find_only(&self, i: usize) -> usize {
        let mut p = i;
        while self.parts[p] != p {
            p = self.parts[p]
        };
        p
    }

    pub fn same(&mut self, i: usize, j: usize) -> bool {
        self.find(i) == self.find(j)
    }

    pub fn same_only(&self, i: usize, j: usize) -> bool {
        self.find_only(i) == self.find_only(j)
    }
}

#[inline]
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
    }
}

#[inline]
fn binary_search<F>(l: i64, r: i64, query_fn: F) -> i64 where F: Fn(i64) -> bool {
    let mut size = r - l;
    let mut base = l;
    while size > 1 {
        let half = size / 2;
        let mid = base + half;
        if !query_fn(mid) {
            base = mid;
        }
        size -= half;
    }
    base + !query_fn(base) as i64
}

#[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");
    }
}

#[allow(dead_code)]
fn abc065_b() {
    input! {
        n: usize,
        arr: [usize; n],
    }
    let arr: Vec<usize> = arr;
    let mut cnt: usize = 0;
    let mut visited = vec![false; n];
    let mut pos: usize = 0;

    loop {
        if pos == 1 {
            println!("{}", cnt);
            return;
        }
        if visited[pos] {
            println!("{}", -1);
            return;
        }
        visited[pos] = true;
        cnt += 1;
        pos = arr[pos] - 1;
    }
}

#[allow(dead_code)]
fn arc090_a() {
    input! {
        n: usize,
        line0: [u32; n],
        line1: [u32; n],

    }
    let line0: Vec<u32> = line0;
    let line1: Vec<u32> = line1;

    let res = (0..n)
        .map(|i| {
            let sum0: u32 = line0[0..i + 1].iter().sum();
            let sum1: u32 = line1[i..n].iter().sum();
            sum0 + sum1
        })
        .max()
        .unwrap();

    println!("{}", res);
}

#[allow(dead_code)]
fn arc098_a() {
    input! {
        n: usize,
        arr: chars,
    }
    let arr: Vec<char> = arr;
    let mut w_sum_arr: Vec<usize> = vec![0; n + 1];
    let mut w_sum = 0;

    for i in 1..n + 1 {
        if arr[i - 1] == 'W' {
            w_sum += 1;
        }
        w_sum_arr[i] = w_sum;
    }

    let res = w_sum_arr[0..n].iter()
        .enumerate()
        .map(|(idx, &w_sum)| {
            let e_sum = n - w_sum_arr[n] - (idx + 1 - w_sum_arr[idx + 1]);
//            println!("{} {} {}", idx, w_sum, e_sum);
            w_sum + e_sum
        })
        .min()
        .unwrap();

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

#[allow(dead_code)]
fn arc098_a2() {
    input! {
        n: usize,
        arr: chars,
    }
    let arr: Vec<char> = arr;

    let w_sum_arr: Vec<usize> = (0..n)
        .scan(0, |state, i| {
            let x = *state;
            if arr[i] == 'W' {
                *state += 1;
            }
            Some(x)
        })
        .collect();

    let e_sum_arr: Vec<usize> = (0..n)
        .rev()
        .scan(0, |state, i| {
            let x = *state;
            if arr[i] == 'E' {
                *state += 1;
            }
            Some(x)
        })
        .collect();

    let res = w_sum_arr.iter()
        .zip(e_sum_arr.iter().rev())
        .map(|(w, e)| w + e)
        .min()
        .unwrap();

//    println!("{:?}", w_sum_arr);
//    println!("{:?}", e_sum_arr);
    println!("{:?}", res);
}

#[allow(dead_code)]
fn abc079_c() {
    input! {
        arr: chars,
    }
    let arr: Vec<char> = arr;
    let arr: Vec<i32> = arr.iter()
        .map(|&x| x.to_digit(10).unwrap() as i32)
        .collect();

    fn int_to_str(x: i32) -> String {
        if x >= 0 { format!("+{}", x) } else { format!("{}", x) }
    }

    for &i in [-1, 1].iter() {
        for &j in [-1, 1].iter() {
            for &k in [-1, 1].iter() {
                let a = arr[0];
                let b = arr[1] * i;
                let c = arr[2] * j;
                let d = arr[3] * k;
                if a + b + c + d == 7 {
                    let b = int_to_str(b);
                    let c = int_to_str(c);
                    let d = int_to_str(d);
                    println!("{}{}{}{}=7", a, b, c, d);
                    return;
                }
            }
        }
    }
}

#[allow(dead_code)]
fn arc084_a() {
    input! {
        n: usize,
        arr_a: [usize; n],
        arr_b: [usize; n],
        arr_c: [usize; n],
    }
    let n: usize = n;
    let mut arr_a: Vec<usize> = arr_a;
    let mut arr_b: Vec<usize> = arr_b;
    let mut arr_c: Vec<usize> = arr_c;

    arr_a.sort();
    arr_b.sort();
    arr_c.sort();

    let res: usize = arr_b.iter()
        .map(|b| {
            arr_a.lower_bound(b) * (n - arr_c.upper_bound(b))
        })
        .sum();

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

#[allow(dead_code)]
fn arc037_c() {
    input! {
        n: usize,
        k: usize,
        rows: [usize; n],
        cols: [usize; n],
    }
    let n: usize = n;
    let k: usize = k;
    let mut rows: Vec<usize> = rows;
    let mut cols: Vec<usize> = cols;

    rows.sort();
    cols.sort();

    let cnt_lte = |n: usize| {
        rows.iter()
            .map(|&x| {
                cols.upper_bound(&(n / x))
            })
            .sum::<usize>()
    };

    let l = rows[0] * cols[0];
    let r = rows[n - 1] * cols[n - 1];
    let res = binary_search(l as i64, r as i64, |x| cnt_lte(x as usize) >= k);

    println!("{}", res);
}

#[allow(dead_code)]
fn abc023_d() {
    input! {
        n: usize,
        arr: [[usize; 2]; n],
    }
    let n: usize = n;
    let arr: Vec<Vec<usize>> = arr;

    let max_height = arr.iter()
        .map(|a| {
            a[0] + a[1] * n - 1
        })
        .max()
        .unwrap();

    let remaining_times_at = |height: i64| {
        arr.iter()
            .map(|a| {
                (height - a[0] as i64) / a[1] as i64
            })
            .collect::<Vec<i64>>()
    };

    let is_possible_with = |height: i64| {
        let times = remaining_times_at(height);
        let mut times: Vec<(usize, i64)> = times.into_iter().enumerate().collect();
        times.sort_by(|&a, &b| { a.1.cmp(&b.1) });

        let is_possible = times.iter().enumerate()
            .all(|(i, &t)| t.1 >= i as i64);
        let order = times.iter()
            .map(|&(i, _t)| i)
            .collect::<Vec<usize>>();
        (is_possible, order)
    };

    let found_height = binary_search(0, max_height as i64, |x| {
        is_possible_with(x).0
    });

    let order = is_possible_with(found_height).1;
    let res = order.iter().enumerate()
        .map(|(i, &j)| {
            arr[j][0] + arr[j][1] * i
        })
        .max()
        .unwrap();

    println!("{}", res);
}

#[allow(dead_code)]
fn arc050_b() {
    input! {
        n_r: u64,
        n_b: u64,
        x: u64,
        y: u64,
    }
    let n_r: u64 = n_r;
    let n_b: u64 = n_b;
    let x: u64 = x;
    let y: u64 = y;

    let is_possible_to_make = |total: u64| -> bool{
        let mut n_r_remain = n_r;
        let mut n_b_remain = n_b;
        if n_r_remain < total || n_b_remain < total {
            return false;
        }
        n_r_remain -= total;
        n_b_remain -= total;
        n_r_remain / (x - 1) + n_b_remain / (y - 1) >= total
    };

    let l = min(n_r / x, n_b / y);
    let r = (n_r / x + n_b / y) + 1;
    let mut size = r - l;
    let mut base = l;
    while size > 1 {
        let half = size / 2;
        let mid = base + half;
        if is_possible_to_make(mid) {
            base = mid;
        }
        size -= half;
    }

    println!("{}", base);
}

#[allow(dead_code)]
fn abc026_d() {
    input! {
        a: f64,
        b: f64,
        c: f64,
    }
    let a: f64 = a;
    let b: f64 = b;
    let c: f64 = c;

    let query = |t: f64| -> f64 {
        a * t + b * (c * t * PI).sin()
    };

    let l = (100. - b) / a;
    let r = (100. + b) / a;
    let mut size = r - l;
    let mut base = l;
    while (query(base) - 100.).abs() > 1e-6 {
        let half = size / 2.;
        let mid = base + half;
        if query(mid) < 100. {
            base = mid;
        }
        size -= half;
    }

    println!("{}", base);
}

#[allow(dead_code)]
fn codefestival_2015_qual_a_d() {
    input! {
        n: i64,
        m: i64,
        arr: [i64; m],
    }
    let n: i64 = n;
    let arr: Vec<i64> = arr;

    let query = |t: i64| {
        let mut boundary = 0;

        for &a in &arr {
            let mut dist = a - boundary - 1;
            if dist < 0 {
                dist = 0;
            }
            if dist > t {
                return false;
            }
            let b0 = max(boundary, a + t - dist * 2);
            let b1 = a + (t - dist) / 2;
            boundary = max(b0, b1);
        }

        return boundary >= n;
    };

    let l = 0;
    let r = n * 2;
    let mut size = r - l + 1;
    let mut base = l;
    while size > 1 {
        let half = size / 2;
        let mid = base + half;
        if !query(mid) {
            base = mid;
        }
        size -= half;
    }

    println!("{}", base + !query(base) as i64);
}

#[allow(dead_code)]
fn abc034_d() {
    input! {
        n: usize,
        k: usize,
        arr: [[f64; 2]; n],
    }
    let k: usize = k;
    let arr: Vec<Vec<f64>> = arr;

    let query = |x: f64| {
        let mut items: Vec<f64> = arr.iter()
            .map(|a| {
                a[0] * (a[1] - x)
            })
            .collect();
        items.sort_by(|a, b| b.partial_cmp(a).unwrap());
        items[..k].iter().sum::<f64>() >= 0.
    };

    let l = 0.;
    let r = 100.;
    let mut size = r - l;
    let mut base = l;
    while size > 1e-6 {
        let half = size / 2.;
        let mid = base + half;
        if query(mid) {
            base = mid;
        }
        size -= half;
    }

    println!("{}", base);
}

#[allow(dead_code)]
fn arc026_4() {
    input! {
        n: usize,
        m: usize,
        arr: [(usize, usize, f64, f64); m],
    }
    let n: usize = n;
    let arr: Vec<(usize, usize, f64, f64)> = arr;

    struct Edge {
        from: usize,
        to: usize,
        cost: f64,
        time: f64,
    }
    impl Edge {
        fn cost_at(&self, x: f64) -> f64 {
            self.cost - x * self.time
        }
    }

    let mut edges: Vec<Edge> = arr.iter()
        .map(|a| {
            Edge {
                from: a.0,
                to: a.1,
                cost: a.2,
                time: a.3,
            }
        })
        .collect();

    let max_salary = edges.iter()
        .map(|e| {
            e.cost / e.time
        })
        .fold(0., |acc, a| {
            if a > acc {
                a
            } else {
                acc
            }
        });

    let mut query = |x: f64| {
        edges.sort_by(|a, b| {
            let cost_a = a.cost_at(x);
            let cost_b = b.cost_at(x);
            cost_a.partial_cmp(&cost_b).unwrap()
        });

        let mut balance = 0.;
        let mut parity = UnionFind::new(n);

        for e in &edges {
            let cost = e.cost_at(x);
            if !parity.same(e.from, e.to) || cost < 0. {
                parity.union(e.from, e.to);
                balance += cost;
            }
        }

        balance <= 0.
    };

    let l = 0.;
    let r = max_salary;
    let mut size = r - l;
    let mut base = l;
    while size > 1e-3 {
        let half = size / 2.;
        let mid = base + half;
        if !query(mid) {
            base = mid;
        }
        size -= half;
    }
    println!("{}", base);
}

#[allow(dead_code)]
fn arc060_a() {
    input! {
        n: usize,
        avg: i64,
        arr: [i64; n],
    }
    let n: usize = n;
    let avg: i64 = avg;
    let arr: Vec<i64> = arr;

    // left index, sum, number of cards
    type Args = (usize, i64, usize);

    struct Solver {
        arr: Vec<i64>,
        cache: HashMap<Args, usize>,
    }
    impl Solver {
        fn solve(&mut self, args: Args) -> usize {
            if self.cache.contains_key(&args) {
                return *self.cache.get(&args).unwrap();
            }
            let res = self.inner(args);
            self.cache.insert(args, res);
            res
        }

        fn inner(&mut self, args: Args) -> usize {
            let (i, j, k) = args;
            if i == 0 && j == 0 && k == 0 {
                return 1;
            }
            if i >= 1 && j < self.arr[i - 1] {
                return self.solve((i - 1, j, k));
            }
            if i >= 1 && k >= 1 && j >= self.arr[i - 1] {
                let last = self.arr[i - 1];
                let n0 = self.solve((i - 1, j - last, k - 1));
                let n1 = self.solve((i - 1, j, k));
                return n0 + n1;
            }
            0
        }
    }

    let cache = HashMap::new();
    let mut solver = Solver { arr: arr, cache: cache };
    let res: usize = (1..n + 1)
        .map(|m| {
            solver.solve((n, avg * m as i64, m))
        })
        .sum();
    println!("{:?}", res);
}

//#[allow(dead_code)]
//fn practice_dp0() {
////    let n: usize = 3;
////    let arr = vec![7, 5, 3];
////    let total = 10;
//    let n: usize = 2;
//    let arr = vec![9, 7];
//    let total = 6;
//
//    let mut dp = vec![vec![false; total + 1]; n + 1];
//    dp[0][0] = true;
//
//    for i in 0..n {
//        for j in 0..total + 1 {
//            if j >= arr[i] {
//                dp[i + 1][j] = dp[i][j - arr[i]] || dp[i][j];
//            } else {
//                dp[i + 1][j] = dp[i][j];
//            }
//        }
//    }
//
//    println!("{:?}", dp);
//    println!("{:?}", dp[n][total]);
//}
//
//#[allow(dead_code)]
//fn practice_dp1() {
//    let n: usize = 3;
//    let arr = vec![7, 5, 3];
//    let total = 10;
////    let n: usize = 2;
////    let arr = vec![9, 7];
////    let total = 6;
//
//    struct Solver {
//        arr: Vec<i32>,
//        cache: HashMap<(usize, i32), bool>,
//    }
//    impl Solver {
//        fn solve(&mut self, i: usize, j: i32) -> bool {
//            println!("{} {}", i, j);
//            match self.cache.get(&(i, j)) {
//                Some(res) => *res,
//                _ => {
//                    let res = self.inner(i, j);
//                    self.cache.insert((i, j), res);
//                    res
//                }
//            }
//        }
//
//        fn inner(&mut self, i: usize, j: i32) -> bool {
//            if i == 0 && j == 0 {
//                true
//            } else if i <= 0 {
//                false
//            } else if j >= self.arr[i - 1] {
//                self.solve(i - 1, j - self.arr[i - 1]) || self.solve(i - 1, j)
//            } else {
//                self.solve(i - 1, j)
//            }
//        }
//    }
//
//    let cache = HashMap::new();
//    let mut solver = Solver { arr: arr, cache: cache };
//    let res = solver.solve(n, total);
//    println!("{:?}", res);
//}
//
//#[allow(dead_code)]
//fn practice_dp2() {
////    let n: usize = 5;
////    let arr = vec![7, 5, 3, 1, 8];
////    let total = 12;
//    let n: usize = 4;
//    let arr = vec![4, 1, 1, 1];
//    let total = 5;
//
//    type Args = (usize, i32);
//
//    struct Solver {
//        arr: Vec<i32>,
//        cache: HashMap<Args, u64>,
//    }
//    impl Solver {
//        fn solve(&mut self, args: Args) -> u64 {
////            println!("{} {}", i, j);
//            match self.cache.get(&args) {
//                Some(res) => *res,
//                _ => {
//                    let res = self.inner(args);
//                    self.cache.insert(args, res);
//                    res
//                }
//            }
//        }
//
//        fn inner(&mut self, args: Args) -> u64 {
//            let (i, j) = args;
//            if i == 0 && j == 0 {
//                return 1;
//            }
//            if i == 0 {
//                return 0;
//            }
//            if j >= self.arr[i - 1] {
//                return self.solve((i - 1, j - self.arr[i - 1])) + self.solve((i - 1, j));
//            }
//            self.solve((i - 1, j))
//        }
//    }
//
//    let cache = HashMap::new();
//    let mut solver = Solver { arr: arr, cache: cache };
//    let res = solver.solve((n, total));
//    println!("{:?}", res);
//}

fn main() {
    arc060_a()
}