{"raw_statement":[{"iden":"problem statement","content":"Given are integers $N$ and $M$. Find the number, modulo $(10^9+7)$, of length-$N$ sequences $(A_1,A_2,\\ldots,A_N)$ that consist of non-negative integers and satisfy the following conditions:\n\n*   $A_1+A_2+\\ldots +A_N = M$;\n*   For every $i$ ($2 \\leq i \\leq N-1$), $2 A_i \\leq A_{i-1} + A_{i+1}$."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 10^5$\n*   $1 \\leq M \\leq 10^5$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $M$"},{"iden":"sample input 1","content":"3 3"},{"iden":"sample output 1","content":"7\n\nThe following seven sequences satisfy the conditions.\n\n*   $0,0,3$\n*   $0,1,2$\n*   $1,0,2$\n*   $1,1,1$\n*   $2,0,1$\n*   $2,1,0$\n*   $3,0,0$"},{"iden":"sample input 2","content":"10 100"},{"iden":"sample output 2","content":"10804516"},{"iden":"sample input 3","content":"10000 100000"},{"iden":"sample output 3","content":"694681734"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}