Submission #1795182

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Source Code Expand

import std.algorithm, std.conv, std.range, std.stdio, std.string;

const mod = 10^^9+7;
alias mint = FactorRing!(mod, true);

void main()
{
  auto rd = readln.split.to!(int[]), n = rd[0], k = rd[1];
  auto s = readln.chomp;

  auto dp = new mint[][](k*2+3, k*2+3), dp2 = new mint[][](k*2+3, k*2+3);
  dp[k+1][k+1] = 1;

  foreach (i; 0..n) {
    foreach (j1; -k..k+1)
      foreach (j2; -k..k+1)
        dp2[j1+k+1][j2+k+1] = 0;

    foreach (j1; -k..k+1)
      foreach (j2; -k..k+1) {
        if (s[i] == '0' || s[i] == '?')
          dp2[j1-1+k+1][(j2-1 >= 0 ? -1 : j2-1)+k+1] += dp[j1+k+1][j2+k+1];
        if (s[i] == '1' || s[i] == '?')
          dp2[(j1+1 <= 0 ? 1 : j1+1)+k+1][j2+1+k+1] += dp[j1+k+1][j2+k+1];
      }

    foreach (j; -k..k+1) dp[j+k+1][] = dp2[j+k+1][];
  }

  auto ans = mint(0);
  foreach (j1; -k..k+1)
    foreach (j2; -k..k+1)
      ans += dp[j1+k+1][j2+k+1];

  writeln(ans);
}

struct FactorRing(int m, bool pos = false)
{
  version(BigEndian) {
    union { long vl; struct { int vi2; int vi; } }
  } else {
    union { long vl; int vi; }
  }

  static init() { return FactorRing!(m, pos)(0); }

  @property int toInt() { return vi; }
  alias toInt this;

  this(int v) { vi = v; }
  this(int v, bool runMod) { vi = runMod ? mod(v) : v; }
  this(long v) { vi = mod(v); }

  ref FactorRing!(m, pos) opAssign(int v) { vi = v; return this; }

  pure auto mod(int v) const
  {
    static if (pos) return v % m;
    else return (v % m + m) % m;
  }

  pure auto mod(long v) const
  {
    static if (pos) return cast(int)(v % m);
    else return cast(int)((v % m + m) % m);
  }

  static if (!pos) {
    pure auto opUnary(string op: "-")() const { return FactorRing!(m, pos)(mod(-vi)); }
  }

  static if (m < int.max / 2) {
    pure auto opBinary(string op: "+")(int rhs) const { return FactorRing!(m, pos)(mod(vi + rhs)); }
    pure auto opBinary(string op: "-")(int rhs) const { return FactorRing!(m, pos)(mod(vi - rhs)); }
  } else {
    pure auto opBinary(string op: "+")(int rhs) const { return FactorRing!(m, pos)(mod(vl + rhs)); }
    pure auto opBinary(string op: "-")(int rhs) const { return FactorRing!(m, pos)(mod(vl - rhs)); }
  }
  pure auto opBinary(string op: "*")(int rhs) const { return FactorRing!(m, pos)(mod(vl * rhs)); }

  pure auto opBinary(string op)(FactorRing!(m, pos) rhs) const
    if (op == "+" || op == "-" || op == "*") { return opBinary!op(rhs.vi); }

  static if (m < int.max / 2) {
    auto opOpAssign(string op: "+")(int rhs) { vi = mod(vi + rhs); }
    auto opOpAssign(string op: "-")(int rhs) { vi = mod(vi - rhs); }
  } else {
    auto opOpAssign(string op: "+")(int rhs) { vi = mod(vl + rhs); }
    auto opOpAssign(string op: "-")(int rhs) { vi = mod(vl - rhs); }
  }
  auto opOpAssign(string op: "*")(int rhs) { vi = mod(vl * rhs); }

  auto opOpAssign(string op)(FactorRing!(m, pos) rhs)
    if (op == "+" || op == "-" || op == "*") { return opOpAssign!op(rhs.vi); }
}

Submission Info

Judge Result