import std.conv, std.functional, std.range, std.stdio, std.string;
import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, std.regex, std.typecons;
import core.bitop;

class EOFException : Throwable { this() { super("EOF"); } }
string[] tokens;
string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; }
int readInt() { return readToken.to!int; }
long readLong() { return readToken.to!long; }
real readReal() { return readToken.to!real; }

bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } }
bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } }

int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; }
int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); }
int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); }


struct ModInt(int M_) {
  import std.conv : to;
  alias M = M_;
  int x;
  this(ModInt a) { x = a.x; }
  this(long a) { x = cast(int)(a % M); if (x < 0) x += M; }
  ref ModInt opAssign(long a) { return (this = ModInt(a)); }
  ref ModInt opOpAssign(string op)(ModInt a) {
    static if (op == "+") { x += a.x; if (x >= M) x -= M; }
    else static if (op == "-") { x -= a.x; if (x < 0) x += M; }
    else static if (op == "*") { x = cast(int)((cast(long)(x) * a.x) % M); }
    else static if (op == "/") { this *= a.inv(); }
    else static assert(false);
    return this;
  }
  ref ModInt opOpAssign(string op)(long a) {
    static if (op == "^^") {
      if (a < 0) return (this = inv()^^(-a));
      ModInt t2 = this, te = ModInt(1);
      for (long e = a; e > 0; e >>= 1) {
        if (e & 1) te *= t2;
        t2 *= t2;
      }
      x = cast(int)(te.x);
      return this;
    } else return mixin("this " ~ op ~ "= ModInt(a)");
  }
  ModInt inv() const {
    int a = x, b = M, y = 1, z = 0, t;
    for (; ; ) {
      t = a / b; a -= t * b;
      if (a == 0) {
        assert(b == 1 || b == -1);
        return ModInt(b * z);
      }
      y -= t * z;
      t = b / a; b -= t * a;
      if (b == 0) {
        assert(a == 1 || a == -1);
        return ModInt(a * y);
      }
      z -= t * y;
    }
  }
  ModInt opUnary(string op: "-")() const { return ModInt(-x); }
  ModInt opBinary(string op, T)(T a) const {
    return mixin("ModInt(this) " ~ op ~ "= a");
  }
  ModInt opBinaryRight(string op)(long a) const {
    return mixin("ModInt(a) " ~ op ~ "= this");
  }
  bool opCast(T: bool)() const { return (x != 0); }
  string toString() const { return x.to!string; }
}

enum MO = 998244353;
alias Mint = ModInt!MO;


enum LIM = 605;
Mint[] inv, fac, invFac;
void prepare() {
  inv = new Mint[LIM];
  fac = new Mint[LIM];
  invFac = new Mint[LIM];
  inv[1] = 1;
  foreach (i; 2 .. LIM) {
    inv[i] = -(Mint.M / i) * inv[cast(size_t)(Mint.M % i)];
  }
  fac[0] = invFac[0] = 1;
  foreach (i; 1 .. LIM) {
    fac[i] = fac[i - 1] * i;
    invFac[i] = invFac[i - 1] * inv[i];
  }
}
Mint binom(long n, long k) {
  if (0 <= k && k <= n) {
    assert(n < LIM);
    return fac[cast(size_t)(n)] * invFac[cast(size_t)(k)] * invFac[cast(size_t)(n - k)];
  } else {
    return Mint(0);
  }
}



void main() {
  prepare;
  
  try {
    for (; ; ) {
      const S = readToken();
      const K = readInt();
      const L = cast(int)(S.length);
      
      int C;
      auto as = new int[L + 1];
      foreach (i; 0 .. L) {
        if (S[i] == '0') {
          ++C;
        } else {
          ++as[C];
        }
      }
      debug {
        writeln("as = ", as);
      }
      
      // cnt, dest, floating
      auto dp = new Mint[][][](C + 1 + 1, C + 1 + 1, L + 1);
      dp[0][0][0] = 1;
      foreach (c; 0 .. C + 1) {
        foreach (d; 0 .. C + 1 + 1) {
          auto sub = new Mint[][](as[c] + 1, d + 1);
          sub[0][d] = 1;
          foreach (j; 0 .. as[c]) {
            foreach (x; 1 .. d + 1) {
              if (sub[j][x]) {
                foreach (y; 1 .. x + 1) {
                  sub[j + 1][y] += sub[j][x];
                }
              }
            }
          }
          debug {
            if (L <= 10) {
              writefln("sub[%s][%s] = %s", c, d, sub);
            }
          }
          foreach (f; 0 .. L + 1) {
            if (dp[c][d][f]) {
              Mint mul = 1;
              // skip
              dp[c + 1][d + 1][f] += dp[c][d][f];
              // use
              foreach (j; 1 .. as[c] + 1) {
                foreach (x; 1 .. d + 1) {
                  if (sub[j][x]) {
                    dp[c + 1][x][f + j] += dp[c][d][f] * sub[j][x];
                  }
                }
              }
            }
          }
        }
      }
      debug {
        if (L <= 10) {
          foreach (c; 0 .. C + 1 + 1) {
            writeln(c, ": ", dp[c]);
          }
        }
      }
      
      Mint ans;
      foreach (d; 0 .. C + 1 + 1) foreach (f; 0 .. L + 1) {
        if (dp[C + 1][d][f]) {
          if (f <= K) {
            ans += dp[C + 1][d][f];
          }
        }
      }
      writeln(ans);
    }
  } catch (EOFException e) {
  }
}


Measured memory_bytes: 170732