#[allow(unused_imports)]
use std::cmp::{max, min};
use std::collections::*;
use std::fmt::Display;
use std::io::{stdin, Read};
use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Sub, SubAssign};
use std::str::FromStr;
pub const MOD: usize = 998244353;

#[derive(Clone, Copy, PartialEq, Debug, Default)]
pub struct Mint<T>(pub T);

impl Mint<usize> {
    pub fn pow(self, exp: usize) -> Self {
        let mut exp = exp;
        let mut v = self;
        let mut ret = Mint(1);
        while exp > 0 {
            if exp & 1 == 1 {
                ret *= v;
            }
            v *= v;
            exp >>= 1;
        }
        ret
    }
    pub fn inv(self) -> Self {
        self.pow(MOD - 2)
    }
}

impl<T: Display + Copy + PartialEq> Display for Mint<T> {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        write!(f, "{}", self.0)
    }
}

impl<T: FromStr + Copy + PartialEq> FromStr for Mint<T> {
    type Err = T::Err;
    fn from_str(s: &str) -> Result<Self, Self::Err> {
        let v = T::from_str(s)?;
        Ok(Mint(v))
    }
}

impl Add<usize> for Mint<usize> {
    type Output = Self;
    fn add(self, rhs: usize) -> Self::Output {
        Mint((self.0 + rhs) % MOD)
    }
}

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

impl AddAssign<usize> for Mint<usize> {
    fn add_assign(&mut self, rhs: usize) {
        *self = *self + rhs;
    }
}

impl AddAssign for Mint<usize> {
    fn add_assign(&mut self, rhs: Self) {
        *self = *self + rhs;
    }
}

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

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

impl SubAssign<usize> for Mint<usize> {
    fn sub_assign(&mut self, rhs: usize) {
        *self = *self - rhs
    }
}

impl SubAssign for Mint<usize> {
    fn sub_assign(&mut self, rhs: Self) {
        *self = *self - rhs
    }
}

impl Mul<usize> for Mint<usize> {
    type Output = Self;
    fn mul(self, rhs: usize) -> Self::Output {
        Mint((self.0 * rhs) % MOD)
    }
}

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

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

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

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

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

impl DivAssign<usize> for Mint<usize> {
    fn div_assign(&mut self, rhs: usize) {
        *self = *self / rhs;
    }
}
impl DivAssign for Mint<usize> {
    fn div_assign(&mut self, rhs: Self) {
        *self = *self / rhs;
    }
}

#[allow(unused_macros)]
macro_rules! parse {
    ($it: ident ) => {};
    ($it: ident, ) => {};
    ($it: ident, $var:ident : $t:tt $($r:tt)*) => {
        let $var = parse_val!($it, $t);
        parse!($it $($r)*);
    };
    ($it: ident, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = parse_val!($it, $t);
        parse!($it $($r)*);
    };
}

#[allow(unused_macros)]
macro_rules! parse_val {
    ($it: ident, [$t:tt; $len:expr]) => {
        (0..$len).map(|_| parse_val!($it, $t)).collect::<Vec<_>>();
    };
    ($it: ident, ($($t: tt),*)) => {
        ($(parse_val!($it, $t)),*)
    };
    ($it: ident, u1) => {
        $it.next().unwrap().parse::<usize>().unwrap() -1
    };
    ($it: ident, $t: ty) => {
        $it.next().unwrap().parse::<$t>().unwrap()
    };
}

fn solve(s: &str) {
    let mut it = s.split_whitespace();
    let s = it.next().unwrap();
    parse!(it, K: usize);
    let mut v = s.bytes().fold(vec![0usize], |mut v, x| {
        if x == b'0' {
            v.push(0);
        } else {
            *v.last_mut().unwrap() += 1;
        }
        v
    });
    let K = min(K, v.iter().sum());
    v.reverse();
    let n = v.len();
    let mut dp = vec![vec![vec![0usize; K + 1]; K + 1]; n];
    dp[0][0][0] = 1;
    for i in 0..(n - 1) {
        for j in 0..=K {
            for k in 0..=K {
                let tmp = dp[i][j][k];
                for l in 0..=k {
                    let t = dp[i + 1][j].get_mut(k - l).unwrap();
                    *t += tmp;
                    if *t >= MOD {
                        *t %= MOD;
                    }
                }
                for l in 1..=min(v[i], min(K - j, K - k)) {
                    let t = dp[i + 1][j + l].get_mut(k + l).unwrap();
                    *t += tmp;
                    if *t >= MOD {
                        *t %= MOD;
                    }
                }
            }
        }
    }

    let mut ret = 0;
    for i in 0..=K {
        for j in 0..=K {
            ret += dp[n - 1][i][j];
            ret %= MOD;
        }
    }
    println!("{}", ret);
}

fn main() {
    let mut s = String::new();
    stdin().read_to_string(&mut s).unwrap();
    solve(&s);
}

#[cfg(test)]
mod tests {
    use super::*;
    #[test]
    fn test_input() {
        let s = "
        ";
        solve(s);
    }
}


Measured memory_bytes: 29472