{"raw_statement":[{"iden":"problem statement","content":"Consider a sequence of length $N$ consisting of `0`s and `1`s, $A=(A_1,A_2,\\dots,A_N)$, that satisfies the following condition.\n\n> For every $i=1,2,\\dots,M$, there are at least $X_i$ occurrences of `1` among $A_{L_i}, A_{L_i+1}, \\dots, A_{R_i}$.\n\nPrint one such sequence with the **fewest** number of occurrences of `1`s.\nThere always exists a sequence that satisfies the condition under the Constraints."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 2 \\times 10^5$\n*   $1 \\leq M \\leq \\min(2 \\times 10^5, \\frac{N(N+1)}{2} )$\n*   $1 \\leq L_i \\leq R_i \\leq N$\n*   $1 \\leq X_i \\leq R_i-L_i+1$\n*   $(L_i,R_i) \\neq (L_j,R_j)$ if $i \\neq j$.\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $M$\n$L_1$ $R_1$ $X_1$\n$L_2$ $R_2$ $X_2$\n$\\vdots$\n$L_M$ $R_M$ $X_M$"},{"iden":"sample input 1","content":"6 3\n1 4 3\n2 2 1\n4 6 2"},{"iden":"sample output 1","content":"0 1 1 1 0 1 \n\nAnother acceptable output is `1 1 0 1 1 0`.  \nOn the other hand, `0 1 1 1 1 1`, which has more than the fewest number of `1`s, is unacceptable."},{"iden":"sample input 2","content":"8 2\n2 6 1\n3 5 3"},{"iden":"sample output 2","content":"0 0 1 1 1 0 0 0"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}