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;
        }
      }
      
      if (N >= 2 && A[0] == 1) {
        const lb = cast(int)(prod - 1);
        foreach (x; 1 .. lb) {
          write(0);
        }
        foreach (x; lb .. X + 1) {
          write(1);
        }
        writeln();
        goto failed;
      }
      
      {
        auto ms = new int[1 << N];
        auto dp = new int[][1 << N];
        foreach (u; 0 .. 1 << N) {
          ms[u] = 1;
          foreach (i; 0 .. N) {
            if (u & 1 << i) {
              ms[u] = ms[u] / gcd(ms[u], A[i]) * A[i];
            }
          }
          dp[u] = new int[ms[u]];
          dp[u][] = INF;
          if (!(u & u - 1)) {
            chmin(dp[u][0], ms[u]);
          }
        }
        foreach (u; 1 .. 1 << N) {
          foreach (i; 0 .. N) {
            if (!(u & 1 << i)) {
              const v = u | 1 << i;
              alias Entry = Tuple!(int, "c", int, "s");
              BinaryHeap!(Array!Entry, "a > b") que;
              auto costs = new int[ms[v]];
              costs[] = INF;
              foreach (r; 0 .. ms[u]) {
                if (dp[u][r] < INF) {
                  const z = (dp[u][r] + 1) * (A[i] + 1) - 1;
                  const s = z % ms[v];
                  if (chmin(costs[s], z)) {
                    que.insert(Entry(z, s));
                  }
                }
              }
              for (; !que.empty; ) {
                const c = que.front.c;
                const s = que.front.s;
                que.removeFront;
                if (costs[s] == c) {
                  foreach (d; (u & u - 1) ? [ms[u] * (A[i] + 1), A[i]] : [A[i]]) {
                    const ss = (s + d) % ms[v];
                    if (chmin(costs[ss], c + d)) {
                      que.insert(Entry(c + d, ss));
                    }
                  }
                }
              }
              foreach (s; 0 .. ms[v]) {
                chmin(dp[v][s], costs[s]);
              }
            }
          }
          debug {
            writeln(u, " ", ms[u], " ", dp[u]);
          }
        }
        
        auto ans = new char[X + 1];
        ans[] = '0';
        foreach (r; 0 .. ms[$ - 1]) {
          if (dp[$ - 1][r] < INF) {
            for (int x = dp[$ - 1][r]; x <= X; ) {
              ans[x] = '1';
              if (N == 1) {
                break;
              }
              x += ms[$ - 1];
            }
          }
        }
        writeln(ans[1 .. $]);
      }
     failed:
    }
  } catch (EOFException e) {
  }
}