Problem:
Score : 800 points

Problem Statement

Given is a string S consisting of 0 and 1. Find the number of strings, modulo 998244353, that can result from applying the following operation on S between 0 and K times (inclusive):

Choose a pair of integers i, j (1\leq i < j\leq |S|) such that the i-th and j-th characters of S are 0 and 1, respectively. Remove the j-th character from S and insert it to the immediate left of the i-th character.

Constraints

1 \leq |S| \leq 300

0 \leq K \leq 10^9

S consists of 0 and 1.

Input

Input is given from Standard Input in the following format:

S K

Output

Find the number of strings, modulo 998244353, that can result from applying the operation on S between 0 and K times (inclusive).

Sample Input 1

0101 1

Sample Output 1

4

Four strings, 0101, 0110, 1001, and 1010, can result.

Sample Input 2

01100110 2

Sample Output 2

14

Sample Input 3

1101010010101101110111100011011111011000111101110101010010101010101 20

Sample Output 3

113434815

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

#![allow(unused_imports)]
#![allow(non_snake_case, unused)]

use std::cmp::*;
use std::collections::*;
use std::ops::*;

// https://atcoder.jp/contests/hokudai-hitachi2019-1/submissions/10518254

macro_rules! eprint {
	($($t:tt)*) => {{
		use ::std::io::Write;
		let _ = write!(::std::io::stderr(), $($t)*);
	}};
}
macro_rules! eprintln {
	() => { eprintln!(""); };
	($($t:tt)*) => {{
		use ::std::io::Write;
		let _ = writeln!(::std::io::stderr(), $($t)*);
	}};
}
macro_rules! dbg {
	($v:expr) => {{
		let val = $v;
		eprintln!("[{}:{}] {} = {:?}", file!(), line!(), stringify!($v), val);
		val
	}}
}

macro_rules! mat {
	($($e:expr),*) => { Vec::from(vec![$($e),*]) };
	($($e:expr,)*) => { Vec::from(vec![$($e),*]) };
	($e:expr; $d:expr) => { Vec::from(vec![$e; $d]) };
	($e:expr; $d:expr $(; $ds:expr)+) => { Vec::from(vec![mat![$e $(; $ds)*]; $d]) };
}

macro_rules! ok {
	($a:ident$([$i:expr])*.$f:ident()$(@$t:ident)*) => {
		$a$([$i])*.$f($($t),*)
	};
	($a:ident$([$i:expr])*.$f:ident($e:expr$(,$es:expr)*)$(@$t:ident)*) => { {
		let t = $e;
		ok!($a$([$i])*.$f($($es),*)$(@$t)*@t)
	} };
}

pub fn readln() -> String {
	let mut line = String::new();
	::std::io::stdin().read_line(&mut line).unwrap_or_else(|e| panic!("{}", e));
	line
}

macro_rules! read {
	($($t:tt),*; $n:expr) => {{
		let stdin = ::std::io::stdin();
		let ret = ::std::io::BufRead::lines(stdin.lock()).take($n).map(|line| {
			let line = line.unwrap();
			let mut it = line.split_whitespace();
			_read!(it; $($t),*)
		}).collect::<Vec<_>>();
		ret
	}};
	($($t:tt),*) => {{
		let line = readln();
		let mut it = line.split_whitespace();
		_read!(it; $($t),*)
	}};
}

macro_rules! _read {
	($it:ident; [char]) => {
		_read!($it; String).chars().collect::<Vec<_>>()
	};
	($it:ident; [u8]) => {
		Vec::from(_read!($it; String).into_bytes())
	};
	($it:ident; usize1) => {
		$it.next().unwrap_or_else(|| panic!("input mismatch")).parse::<usize>().unwrap_or_else(|e| panic!("{}", e)) - 1
	};
	($it:ident; [usize1]) => {
		$it.map(|s| s.parse::<usize>().unwrap_or_else(|e| panic!("{}", e)) - 1).collect::<Vec<_>>()
	};
	($it:ident; [$t:ty]) => {
		$it.map(|s| s.parse::<$t>().unwrap_or_else(|e| panic!("{}", e))).collect::<Vec<_>>()
	};
	($it:ident; $t:ty) => {
		$it.next().unwrap_or_else(|| panic!("input mismatch")).parse::<$t>().unwrap_or_else(|e| panic!("{}", e))
	};
	($it:ident; $($t:tt),+) => {
		($(_read!($it; $t)),*)
	};
}


pub fn main() {
	let _ = ::std::thread::Builder::new().name("run".to_string()).stack_size(32 * 1024 * 1024).spawn(run).unwrap().join();
}

const MOD: usize = 998244353;
const INF: i64 = std::i64::MAX/3;

use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Sub, SubAssign};

type Num = usize;

#[derive(Clone, Copy, Debug)]
pub struct ModInt<T: Copy + Clone>(pub T);

impl Add<ModInt<Num>> for ModInt<Num> {
    type Output = ModInt<Num>;
    fn add(self, rhs: ModInt<Num>) -> ModInt<Num> {
        self + rhs.0
    }
}

impl Add<Num> for ModInt<Num> {
    type Output = ModInt<Num>;
    fn add(self, rhs: Num) -> ModInt<Num> {
        let mut t = rhs + self.0;
        if t >= MOD {
            t = t - MOD;
        }
        ModInt(t)
    }
}

impl Sub<Num> for ModInt<Num> {
    type Output = ModInt<Num>;
    fn sub(self, rhs: Num) -> ModInt<Num> {
        let rhs = if rhs >= MOD { rhs % MOD } else { rhs };
        let value = if self.0 < rhs { self.0 + MOD } else { self.0 };
        ModInt(value - rhs)
    }
}

impl Sub<ModInt<Num>> for ModInt<Num> {
    type Output = ModInt<Num>;
    fn sub(self, rhs: ModInt<Num>) -> ModInt<Num> {
        self - rhs.0
    }
}

impl AddAssign<Num> for ModInt<Num> {
    fn add_assign(&mut self, other: Num) {
        *self = *self + other;
    }
}
impl AddAssign<ModInt<Num>> for ModInt<Num> {
    fn add_assign(&mut self, other: ModInt<Num>) {
        *self = *self + other;
    }
}

impl SubAssign<Num> for ModInt<Num> {
    fn sub_assign(&mut self, other: Num) {
        *self = *self - other;
    }
}

impl SubAssign<ModInt<Num>> for ModInt<Num> {
    fn sub_assign(&mut self, other: ModInt<Num>) {
        *self = *self - other;
    }
}

impl Div<Num> for ModInt<Num> {
    type Output = ModInt<Num>;
    fn div(self, rhs: Num) -> ModInt<Num> {
        self * ModInt(rhs).pow(MOD - 2)
    }
}

impl Div<ModInt<Num>> for ModInt<Num> {
    type Output = ModInt<Num>;
    fn div(self, rhs: ModInt<Num>) -> ModInt<Num> {
        self / rhs.0
    }
}

impl DivAssign<Num> for ModInt<Num> {
    fn div_assign(&mut self, rhs: Num) {
        *self = *self / rhs
    }
}
impl DivAssign<ModInt<Num>> for ModInt<Num> {
    fn div_assign(&mut self, rhs: ModInt<Num>) {
        *self = *self / rhs
    }
}

impl Mul<ModInt<Num>> for ModInt<Num> {
    type Output = ModInt<Num>;

    fn mul(self, rhs: ModInt<Num>) -> ModInt<Num> {
        self * rhs.0
    }
}
impl Mul<Num> for ModInt<Num> {
    type Output = ModInt<Num>;

    fn mul(self, rhs: Num) -> ModInt<Num> {
        let t = (self.0 * rhs) % MOD;
        ModInt(t)
    }
}

impl MulAssign<Num> for ModInt<Num> {
    fn mul_assign(&mut self, rhs: Num) {
        *self = *self * rhs;
    }
}

impl MulAssign<ModInt<Num>> for ModInt<Num> {
    fn mul_assign(&mut self, rhs: ModInt<Num>) {
        *self = *self * rhs;
    }
}

impl ModInt<Num> {
    pub fn pow(self, e: usize) -> ModInt<Num> {
        let mut result = ModInt(1);
        let mut cur = self;
        let mut e = e;
        while e > 0 {
            if e & 1 == 1 {
                result *= cur;
            }
            e >>= 1;
            cur *= cur;
        }
        result
    }
}

pub struct Comb {
    fact: Vec<ModInt<Num>>,
    factinv: Vec<ModInt<Num>>,
}

impl Comb {
    /// Create a object that provides effiecint computation of combinations
    /// for input smaller than `n`.
    ///
    /// This requires `O(n)` time.
    pub fn new(n: usize) -> Comb {
        let mut fact: Vec<ModInt<Num>> = vec![ModInt(0); n + 1];
        let mut factinv: Vec<ModInt<Num>> = vec![ModInt(0); n + 1];
        fact[0] = ModInt(1);
        for i in 0..n {
            fact[i + 1] = fact[i] * (i + 1);
        }
        factinv[n] = fact[n].pow(MOD-2);
        for i in (0..n).rev() {
            factinv[i] = factinv[i + 1] * (i + 1);
        }
        Comb {
            fact: fact,
            factinv: factinv,
        }
    }

    /// `n! = 1 * 2 * ... * n`
    ///
    /// `O(1)` if n is smaller than input in `new` method.
    pub fn fact(&self, n: usize) -> ModInt<Num> {
        if let Some(x) = self.fact.get(n as usize) {
            *x
        } else if n >= MOD {
            ModInt(0)
        } else {
            // Note that this is slow if `n` is large.
            // Precalculation is a possible solution but doesn't work for any module number.
            let mut res = ModInt(1);
            for a in 1..(n + 1) {
                res *= a;
            }
            res
        }
    }

    /// returns `y` such that `n! * y == 1`.
    ///
    /// `O(1)` if n is smaller than input in `new` method.
    pub fn factinv(&self, n: usize) -> ModInt<Num> {
        if let Some(x) = self.factinv.get(n) {
            *x
        } else {
            self.fact(n).pow(MOD-2)
        }
    }

    /// `nPr = n! / (n - r)!`
    ///
    /// `O(1)` if n and r are smaller than input in `new` method.
    pub fn perm(&self, n: usize, r: usize) -> ModInt<Num> {
        if n >= r {
            self.fact(n) * self.factinv(n - r)
        } else {
            ModInt(0)
        }
    }

    /// `nCr = n! / (n - r)! / r!`.
    ///
    /// `O(1)` if n and r are smaller than input in `new` method.
    pub fn comb(&self, n: usize, r: usize) -> ModInt<Num> {
        let m = MOD;
        if n >= m {
            self.comb(n % m, r % m) * self.comb(n / m, r / m) // Lucas' theorem
        } else if n >= r {
            self.fact(n) * self.factinv(n - r) * self.factinv(r)
        } else {
            ModInt(0)
        }
    }
}

fn solve() {
	let (s,k) = read!(String,i64);
	let c = s.chars().collect::<Vec<char>>();
	let n = c.len();
	let mut prev = c[n-1];
	let mut count = 1;
	let mut z = 1;
	let mut v = vec![];
	for i in (0..n-1).rev() {
		if c[i]=='1' {
			z += 1;
		}
		if c[i+1]==c[i] {
			count += 1;
		}
		else {
			match c[i] {
				'0' => v.push((1,count)),
				_ => v.push((0,count)),
			}
			count = 1;
		}
	}
	match c[0] {
		'0' => v.push((0,count+1)),
		_ => {
			v.push((1,count));
			v.push((0,1));
		},
	}
	let mut dp = vec![vec![vec![ModInt(0);2*z+2];2*z+2];n+2];
	dp[0][0][0] = ModInt(1);
	let mut comb = Comb::new(z+3);
	for (idx,&(val,count)) in v.iter().enumerate() {
		if val==0 {
			let t = count-1;
			if t==0 {
				for x in 0..z+1 {
					for m in 0..z+1 {
						dp[idx+1][x][m] = dp[idx+1][x][m] + dp[idx][x][m];
					}
				}
				continue;
			}
			for i in 0..z+2 {
				for j in 0..z+2 {
					if j>i {
						continue;
					}
					let x = i-j;
					let tmp = comb.comb(t+j-1,j);
					for m in 0..z+1 {
						dp[idx+1][x][m] = dp[idx+1][x][m] + dp[idx][i][m]*tmp;
					}
				}
			}
		}
		if val==1 {
			for i in 0..z+2 {
				for j in 0..z+2 {
					if count+j<i {
						continue;
					}
					let x = j+count-i;
					let p = max(0,count as i64 - i as i64) as usize;
					for m in 0..z+2 {
						dp[idx+1][x][m+p] = dp[idx+1][x][m+p] + dp[idx][j][m];
					}
				}
			}
		}
		// for x in 0..z+2 {
		// 	for m in 0..z+2 {
		// 		print!("{} ",dp[idx+1][x][m].0);
		// 	}
		// 	println!();
		// }
		// println!();
	}
	let mut ans = ModInt(0);
	for i in 0..min((z+2) as i64,k+1) {
		ans += dp[v.len()][0][i as usize];
		// print!("{} ",dp[v.len()][0][i as usize].0);
	}
	println!("{}",ans.0);
}

fn run() {
    solve();
}