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)); }


enum INF = 10^^9;

void main() {
  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];
        foreach (u; 0 .. V) {
          const as = decode(u);
          prods[u] = 1;
          foreach (j; 0 .. m) {
            prods[u] *= (grp[j][0] + 1)^^as[j];
          }
        }
        auto single = new bool[V];
        auto ms = new int[V];
        auto dp = new int[][V];
        foreach (u; 1 .. V) {
          const as = decode(u);
          single[u] = (as.sum == 1);
          ms[u] = 1;
          foreach (j; 0 .. m) {
            if (as[j] > 0) {
              ms[u] = ms[u] / gcd(ms[u], grp[j][0]) * grp[j][0];
            }
          }
          dp[u] = new int[ms[u]];
          dp[u][] = INF;
          if (single[u]) {
            chmin(dp[u][0], ms[u]);
          }
        }
        foreach (u; 1 .. V) {
          const as = decode(u);
          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 (r; 0 .. ms[v]) {
                  if (dp[v][r] < INF) {
                    for (int x = dp[v][r]; ; ) {
                      foreach (s; 0 .. ms[w]) {
                        if (dp[w][s] < INF) {
                          for (int y = dp[w][s]; ; ) {
                            const z0 = (x + 1) * (y + 1) - 1;
                            for (int z = z0; ; ) {
                              chmin(dp[u][z % ms[u]], z);
                              z += x;
                              if ((z - z0) % ms[u] == 0) {
                                break;
                              }
                            }
                            for (int z = z0; ; ) {
                              chmin(dp[u][z % ms[u]], z);
                              z += y;
                              if ((z - z0) % ms[u] == 0) {
                                break;
                              }
                            }
                            if (single[w]) {
                              break;
                            }
                            y += ms[w];
                            if ((y - dp[w][s]) % ms[u] == 0) {
                              break;
                            }
                          }
                        }
                      }
                      if (single[v]) {
                        break;
                      }
                      x += ms[v];
                      if ((x - dp[v][r]) % ms[u] == 0) {
                        break;
                      }
                    }
                  }
                }
              }
              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, " ", ms[u], " ", dp[u]);
          }
        }
        
        auto ans = new char[X + 1];
        ans[] = '0';
        foreach (r; 0 .. ms[V - 1]) {
          if (dp[V - 1][r] < INF) {
            for (int x = dp[V - 1][r]; x <= X; ) {
              ans[x] = '1';
              if (single[V - 1]) {
                break;
              }
              x += ms[V - 1];
            }
          }
        }
        writeln(ans[1 .. $]);
      }
     failed:
    }
  } catch (EOFException e) {
  }
}