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)); }




void main() {
  /*
  debug {
    {
      enum lim = 10;
      enum m = 1000;
      int f(int a, int b) {
        return a * b + a + b;
      }
      foreach (a; 1 .. lim) foreach (b; a .. lim) foreach (c; b .. lim) {
        auto canSum = new char[m];
        canSum[] = '0';
        auto perm = [a, b, c];
        do {
          auto can = new char[m];
          can[] = '0';
          for (int k = 0; ; ++k) {
            const f01 = f(perm[0], perm[1]) + k * perm[0];
            if (f01 >= m) break;
            for (int l = 0; ; ++l) {
              const x = f(f01, perm[2]) + l * f01;
              if (x >= m) break;
              can[x] = canSum[x] = '1';
            }
            for (int l = 0; ; ++l) {
              const x = f(f01, perm[2]) + l * perm[2];
              if (x >= m) break;
              can[x] = canSum[x] = '1';
            }
          }
          // writeln(perm, ": ", can);
        } while (perm.nextPermutation);
        writeln(perm, ": ", canSum);
        const g = gcd(gcd(a, b), c);
        foreach (x; 2 * (a + 1) * (b + 1) * (c + 1) - 1 .. m) {
          assert((canSum[x] == '1') == (x % g == 0));
        }
      }
    }
  }
  //*/
  
  try {
    for (; ; ) {
      const N = readInt();
      const X = readInt();
      auto A = new int[N];
      foreach (i; 0 .. N) {
        A[i] = readInt();
      }
      A.sort;
      
      long prod = 1;
      foreach (i; 0 .. N) {
        prod *= (A[i] + 1);
        if (prod - 1 > X) {
          foreach (x; 1 .. X + 1) {
            write(0);
          }
          writeln();
          goto failed;
        }
      }
      
      {
        const grp = A.group.array;
        const m = cast(int)(grp.length);
        debug {
          writeln("grp = ", grp);
        }
        int encode(int[] as) {
          int key;
          foreach_reverse (j; 0 .. m) {
            key = key * (grp[j][1] + 1) + as[j];
          }
          return key;
        }
        int[] decode(int key) {
          auto as = new int[m];
          foreach (j; 0 .. m) {
            as[j] = key % (grp[j][1] + 1);
            key /= (grp[j][1] + 1);
          }
          return as;
        }
        int V = 1;
        foreach (j; 0 .. m) {
          V *= (grp[j][1] + 1);
        }
        
        auto prods = new int[V];
        auto dp = new bool[][V];
        foreach (u; 1 .. V) {
          const as = decode(u);
          prods[u] = 1;
          foreach (j; 0 .. m) {
            if (as[j] > 0) {
              prods[u] *= (grp[j][0] + 1)^^as[j];
            }
          }
          dp[u] = new bool[prods[u]];
          dp[u][0] = true;
          void dfs(int j, int[] bs, int[] cs) {
            if (j == m) {
              const v = encode(bs);
              const w = encode(cs);
              if (v != 0 && w != 0 && v <= w) {
                foreach (x; 0 .. prods[v]) {
                  if (dp[v][x]) {
                    foreach (y; 0 .. prods[w]) {
                      if (dp[w][y]) {
                        const xx = prods[v] - 1 + x;
                        const yy = prods[w] - 1 + y;
                        auto lb = ((xx + 1) * (yy + 1) - 1) - (prods[u] - 1);
                        for (int z = lb; z < prods[u]; z += xx) {
                          dp[u][z] = true;
                        }
                        for (int z = lb; z < prods[u]; z += yy) {
                          dp[u][z] = true;
                        }
                      }
                    }
                  }
                }
              }
              return;
            }
            for (bs[j] = 0; bs[j] <= as[j]; ++bs[j]) {
              cs[j] = as[j] - bs[j];
              dfs(j + 1, bs, cs);
            }
          }
          dfs(0, new int[m], new int[m]);
          debug {
            writeln(u, " ", as, ": ", prods[u], " ", dp[u]);
          }
        }
        
        auto ans = new char[X + 1];
        ans[] = '0';
        foreach (x; 0 .. prods[V - 1]) {
          if (dp[V - 1][x]) {
            const xx = prods[V - 1] - 1 + x;
            if (xx <= X) {
              ans[xx] = '1';
            }
          }
        }
        if (N >= 2) {
          int g = 0;
          foreach (i; 0 .. N) {
            g = gcd(g, A[i]);
          }
          for (int x = prods[V - 1]; ; x += g) {
            const xx = prods[V - 1] - 1 + x;
            if (xx > X) {
              break;
            }
            ans[xx] = '1';
          }
        }
        writeln(ans[1 .. $]);
      }
     failed:
    }
  } catch (EOFException e) {
  }
}