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 C# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;
using System.Numerics;
using System.Threading;
using System.Runtime.CompilerServices;
using System.Diagnostics;
using static System.Math;
using static System.Array;
using static AtCoder.Sc_out;
using static AtCoder.Tool;
using static AtCoder.ModInt;
namespace AtCoder
{
    class AC
    {
        //const int MOD = 1000000007;
        const int MOD = 998244353;

        const int INF = int.MaxValue / 2;
        const long SINF = long.MaxValue / 2;
        const double EPS = 1e-8;
        static readonly int[] dI = { 0, 1, 0, -1, 1, -1, -1, 1 };
        static readonly int[] dJ = { 1, 0, -1, 0, 1, 1, -1, -1 };
        //static List<List<int>> G = new List<List<int>>();
        //static List<List<Edge>> G = new List<List<Edge>>();
        //static List<Edge> E = new List<Edge>();
        static void Main(string[] args)
        {
            //var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false }; Console.SetOut(sw);

            var th = new Thread(Run, 1 << 26);
            th.Start();
            th.Join();

            //Run();
            Console.Out.Flush();
        }
        static void Run()
        {
            int Testcase = 1;
            for (var _ = 0; _ < Testcase; _++) Solve();
        }
        static void Solve()
        {
            Cin.Input(out string s, out int K);
            int N = s.Length;
            var num = new List<int>();
            int len = 0;
            for (var i = 0; i < N; i++)
            {
                if (s[i] == '0') { num.Add(len); len = 0; }
                else { len++; }
                if (i == N - 1) num.Add(len);
            }
            num.Reverse();

            int L = num.Count();
            int S = num.Sum();
            K = Min(K, S);
            var dp = new ModInt[K + 1][];
            var D1 = new ModInt[K + 1][];//斜め
            var D2 = new ModInt[K + 1][];//直線
            for (var i = 0; i <= K; i++)
            {
                dp[i] = new ModInt[S + 1];
                D1[i] = new ModInt[S + 1];
                D2[i] = new ModInt[S + 1];
            }
            int sum = 0;

            for (var i = 0; i <= L; i++)
            {
                for (var j = 0; j <= K; j++) for (var k = 0; k <= S; k++)
                        dp[j][k] = 0;
                //imos,斜め
                for(var z = 0; z <= K + S; z++)
                {
                    for(var y = 0; y <= z; y++)
                    {
                        //idx: z-y,y
                        if (z - y < K && 0 < y && y <= S) D1[z - y][y] += D1[z - y + 1][y - 1];
                    }
                }
                //imos,直線
                for(var j = 0; j <= K; j++)
                {
                    for(var k = 1; k <= S; k++)
                    {
                        D2[j][k] += D2[j][k - 1];
                    }
                }
                for (var j = 0; j <= K; j++) for (var k = 0; k <= S; k++)
                        dp[j][k] = D1[j][k] + D2[j][k];
                for(var j=0;j<=K;j++)for(var k = 0; k <= S; k++)
                    {
                        D1[j][k] = D2[j][k] = 0;
                    }
                if (i == 0) dp[0][0] = 1;
                //OutL($"i={i}");
                /*for (var j = 0; j <= K; j++)
                {
                    for(var k = 0; k <= S; k++)
                    {
                        Out_One(dp[j][k].value);
                    }
                    Endl();
                }*/
                if (i == L) break;
                int a = num[i];
                sum += a;
                //遷移
                for(var j = 0; j <= K; j++)
                {
                    for(var k = 0; k <= S; k++)
                    {
                        if (dp[j][k].value == 0) continue;

                        //斜め
                        int mn = Min(j + a, K);
                        D1[mn][j + k + a - mn] += dp[j][k];
                        if (j > 0 && k + a + 1 <= S) D1[j - 1][k + a + 1] -= dp[j][k];

                        //直線
                        if (k + a + 1 <= S) D2[j][k + a + 1] += dp[j][k];
                        if (sum + 1 <= S) D2[j][sum + 1] -= dp[j][k];
                    }
                }
            }
            ModInt ans = 0;
            for (var i = 0; i <= K; i++) ans += dp[i][S];
            OutL(ans.value);

        }
        public struct Edge
        {
            public int from;

            public int to;
            public long dist;

            public Edge(int t, long c)
            {
                from = -1;
                to = t;
                dist = c;
            }
            public Edge(int f, int t, long c)
            {
                from = f;
                to = t;
                dist = c;
            }
        }
    }
    struct ModInt
    {
        public long value;
        //private const int MOD = 1000000007;
        private const int MOD = 998244353;
        public ModInt(long value) { this.value = value; }
        public static implicit operator ModInt(long a)
        {
            var ret = a % MOD;
            return new ModInt(ret < 0 ? (ret + MOD) : ret);
        }
        public static ModInt operator +(ModInt a, ModInt b) => (a.value + b.value);
        public static ModInt operator -(ModInt a, ModInt b) => (a.value - b.value);
        public static ModInt operator *(ModInt a, ModInt b) => (a.value * b.value);
        public static ModInt operator /(ModInt a, ModInt b) => a * Modpow(b, MOD - 2);
        public static ModInt operator <<(ModInt a, int n) => (a.value << n);
        public static ModInt operator >>(ModInt a, int n) => (a.value >> n);
        public static ModInt operator ++(ModInt a) => a.value + 1;
        public static ModInt operator --(ModInt a) => a.value - 1;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static ModInt Modpow(ModInt a, long n)
        {
            var k = a;
            ModInt ret = 1;
            while (n > 0)
            {
                if ((n & 1) != 0) ret *= k;
                k *= k;
                n >>= 1;
            }
            return ret;
        }
        private static readonly List<long> Factorials = new List<long>() { 1 };
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static ModInt Fac(long n)
        {
            for (var i = Factorials.Count(); i <= n; i++)
            {
                Factorials.Add((Factorials[i - 1] * i) % MOD);
            }
            return Factorials[(int)n];
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static ModInt nCr(long n, long r)
        {
            return n < r ? 0 : Fac(n) / (Fac(r) * Fac(n - r));
        }
        public static explicit operator int(ModInt a) => (int)a.value;
    }
    static class Cin
    {
        public static string[] ReadSplit => Console.ReadLine().Split();
        public static int[] ReadSplitInt => ConvertAll(Console.ReadLine().Split(), int.Parse);
        public static long[] ReadSplitLong => ConvertAll(Console.ReadLine().Split(), long.Parse);
        public static double[] ReadSplit_Double => ConvertAll(Console.ReadLine().Split(), double.Parse);
        public static string Str => Console.ReadLine();
        public static int Int => int.Parse(Console.ReadLine());
        public static long Long => long.Parse(Console.ReadLine());
        public static double Double => double.Parse(Console.ReadLine());
        public static T Conv<T>(string input)
        {
            if (typeof(T).Equals(typeof(ModInt)))
            {
                return (T)(dynamic)(long.Parse(input));
            }
            return (T)Convert.ChangeType(input, typeof(T));
        }
        public static void Input<T>(out T a) => a = Conv<T>(Console.ReadLine());
        public static void Input<T, U>(out T a, out U b)
        { var q = ReadSplit; a = Conv<T>(q[0]); b = Conv<U>(q[1]); }
        public static void Input<T, U, V>(out T a, out U b, out V c)
        { var q = ReadSplit; a = Conv<T>(q[0]); b = Conv<U>(q[1]); c = Conv<V>(q[2]); }
        public static void Input<T, U, V, W>(out T a, out U b, out V c, out W d)
        { var q = ReadSplit; a = Conv<T>(q[0]); b = Conv<U>(q[1]); c = Conv<V>(q[2]); d = Conv<W>(q[3]); }
        public static void Input<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e)
        { var q = ReadSplit; a = Conv<T>(q[0]); b = Conv<U>(q[1]); c = Conv<V>(q[2]); d = Conv<W>(q[3]); e = Conv<X>(q[4]); }
    }
    static class Sc_out
    {
        public static void OutL(object s) => Console.WriteLine(s);
        public static void Out_Sep<T>(IEnumerable<T> s) => Console.WriteLine(string.Join(" ", s));
        public static void Out_Sep<T>(IEnumerable<T> s, string sep) => Console.WriteLine(string.Join($"{sep}", s));
        public static void Out_Sep(params object[] s) => Console.WriteLine(string.Join(" ", s));
        public static void Out_One(object s) => Console.Write($"{s} ");
        public static void Out_One(object s, string sep) => Console.Write($"{s}{sep}");
        public static void Endl() => Console.WriteLine();
    }
    public static class Tool
    {
        static public void Initialize<T>(ref T[] array, T initialvalue)
        {
            array = ConvertAll(array, x => initialvalue);
        }
        static public void Swap<T>(ref T a, ref T b)
        {
            T keep = a;
            a = b;
            b = keep;
        }
        static public void Display<T>(T[,] array2d, int n, int m)
        {
            for (var i = 0; i < n; i++)
            {
                for (var j = 0; j < m; j++)
                {
                    Console.Write($"{array2d[i, j]} ");
                }
                Console.WriteLine();
            }
        }
        static public long Gcd(long a, long b)
        {
            if (a == 0 || b == 0) return Max(a, b);
            return a % b == 0 ? b : Gcd(b, a % b);
        }
        static public long LPow(int a, int b) => (long)Pow(a, b);
        static public bool Bit(long x, int dig) => ((1L << dig) & x) != 0;
        static public int Sig(long a) => a == 0 ? 0 : (int)(a / Abs(a));
    }
}