Language: C++

/*⠄⢰⣧⣼⣯⠄⣸⣠⣶⣶⣦⣾⠄⠄⠄⠄⡀⠄⢀⣿⣿⠄⠄⠄⢸⡇⠄⠄
⠄⠄⠄⣾⣿⠿⠿⠶⠿⢿⣿⣿⣿⣿⣦⣤⣄⢀⡅⢠⣾⣛⡉⠄⠄⠄⠸⢀⣿⠄
⠄⠄⢀⡋⣡⣴⣶⣶⡀⠄⠄⠙⢿⣿⣿⣿⣿⣿⣴⣿⣿⣿⢃⣤⣄⣀⣥⣿⣿⠄
⠄⠄⢸⣇⠻⣿⣿⣿⣧⣀⢀⣠⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⠄
⠄⢀⢸⣿⣷⣤⣤⣤⣬⣙⣛⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡍⠄⠄⢀⣤⣄⠉⠋⣰
⠄⣼⣖⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢇⣿⣿⡷⠶⠶⢿⣿⣿⠇⢀⣤
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⣶⣥⣴⣿⡗
⢀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠄
⢸⣿⣦⣌⣛⣻⣿⣿⣧⠙⠛⠛⡭⠅⠒⠦⠭⣭⡻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠄
⠘⣿⣿⣿⣿⣿⣿⣿⣿⡆⠄⠄⠄⠄⠄⠄⠄⠄⠹⠈⢋⣽⣿⣿⣿⣿⣵⣾⠃⠄
⠄⠘⣿⣿⣿⣿⣿⣿⣿⣿⠄⣴⣿⣶⣄⠄⣴⣶⠄⢀⣾⣿⣿⣿⣿⣿⣿⠃⠄⠄
⠄⠄⠈⠻⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⠄⣿⣿⡀⣾⣿⣿⣿⣿⣛⠛⠁⠄⠄⠄
⠄⠄⠄⠄⠈⠛⢿⣿⣿⣿⠁⠞⢿⣿⣿⡄⢿⣿⡇⣸⣿⣿⠿⠛⠁⠄⠄⠄⠄⠄
⠄⠄⠄⠄⠄⠄⠄⠉⠻⣿⣿⣾⣦⡙⠻⣷⣾⣿⠃⠿⠋⠁⠄⠄⠄⠄⠄⢀⣠⣴
⣿⣿⣿⣶⣶⣮⣥⣒⠲⢮⣝⡿⣿⣿⡆⣿⡿⠃⠄⠄⠄⠄⠄⠄⠄⣠⣴⣿*/

#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,fma,tune=native")
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")


#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/rope>
using namespace std;
using namespace __gnu_pbds;
using namespace __gnu_cxx;
#define ll long long
#define ii pair<ll,ll>
#define iii pair<ii,ll>
#define fi first
#define se second
#define endl '\n'
#define debug(x) cout << #x << " is " << x << endl;

#define rep(x,start,end) for(auto x=(start)-((start)>(end));x!=(end)-((start)>(end));((start)<(end)?x++:x--))
#define all(x) (x).begin(),(x).end()
#define sz(x) (int)(x).size()

ll MAX(ll a){return a;}
ll MIN(ll a){return a;}
template<typename... Args>
ll MAX(ll a,Args... args){return max(a,MAX(args...));}
template<typename... Args>
ll MIN(ll a,Args... args){return min(a,MIN(args...));}

#define indexed_set tree<ll,null_type,less<ll>,rb_tree_tag,tree_order_statistics_node_update>

mt19937 rng(chrono::system_clock::now().time_since_epoch().count());

const int MOD=998244353;

string s;
int k;

vector<int> nums;

ll fix(ll i){
	i%=MOD;
	if (i<0) i+=MOD;
	return i;
}

ll memo[305][305][305];
ll dp(int i,int used,int left){
	if (i==sz(nums)) return used==0;
	if (memo[i][used][left]!=-1) return memo[i][used][left];
	
	int res=0;
	rep(x,1,305){
		if (305<=used+x || left-x<0) break;
		res=fix(res+dp(i+1,used+x,left-x));
	}
	rep(x,0,nums[i]+1){
		if (used-x<0) break;
		res=fix(res+dp(i+1,used-x,left));
	}
	
	//cout<<i<<" "<<used<<" "<<left<<" "<<res<<endl;
	return memo[i][used][left]=res;
}

int main(){
	ios::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);
	
	memset(memo,-1,sizeof(memo));
	
	cin>>s>>k;
	s+='0';
	
	int curr=0;
	for (auto &it:s){
		if (it=='0'){
			nums.push_back(curr);
			curr=0;
		}
		else{
			curr++;
		}
	}
	
	//for (auto &it:nums) cout<<it<<" ";cout<<endl;
	
	cout<<dp(0,0,min(k,304))<<endl;
}


Compiler output:
In file included from /usr/include/c++/14/string:43,
                 from /usr/include/c++/14/bitset:52,
                 from /usr/include/x86_64-linux-gnu/c++/14/bits/stdc++.h:52,
                 from a.cc:22:
/usr/include/c++/14/bits/allocator.h: In destructor 'std::__cxx11::basic_string<char>::_Alloc_hider::~_Alloc_hider()':
/usr/include/c++/14/bits/allocator.h:182:7: error: inlining failed in call to 'always_inline' 'std::allocator< <template-parameter-1-1> >::~allocator() noexcept [with _Tp = char]': target specific option mismatch
  182 |       ~allocator() _GLIBCXX_NOTHROW { }
      |       ^
In file included from /usr/include/c++/14/string:54:
/usr/include/c++/14/bits/basic_string.h:186:14: note: called from here
  186 |       struct _Alloc_hider : allocator_type // TODO check __is_final
      |              ^~~~~~~~~~~~