Dima's spent much time thinking what present to give to Inna and gave her an empty sequence w. Now they want to fill sequence w with numbers zero and one. For that, they decided to play an amusing game.

Before the game begins, Dima chooses m integers a₁, a₂, ..., a_m (1 ≤ a₁ < a₂ < ... < a_m). Then Inna and Dima start playing, that is, adding numbers to sequence w. Each new number they choose is added to the end of the sequence. At some moments of time Dima feels that the game is going to end too soon (and he wants to play with Inna as long as possible), so he hits a table hard with his fist. At that the a₁-th, a₂-th, a₃-th, ..., a_k-th numbers from the beginning simultaneously fall out of the sequence (the sequence gets k numbers less). Here k is such maximum number that value a_k doesn't exceed the current length of the sequence. If number a₁ is larger than the current length of w, then nothing falls out of the sequence.

You are given the chronological sequence of events in the game. Each event is either adding a number to the end of sequence w or Dima's hit on the table. Calculate the sequence w after all these events happen.