{"raw_statement":[{"iden":"problem statement","content":"Snuke the wizard has $N$ magical lamps numbered $1$ to $N$. The cost of the $i$\\-th lamp is $a_i$. Initially, none of the lamps are lit.\nSnuke has an integer value called MP, which is initially $X$. When Snuke lights a lamp with cost $x$, his MP decreases by $x$. Each time Snuke lights one lamp, the cost of all lamps with cost at least $1$ decreases by $1$.\nThere are $N!$ possible orders to light the lamps. Find the number, modulo $998244353$, of such orders where MP never becomes negative."},{"iden":"constraints","content":"*   $1 \\le N \\le 100$\n*   $0 \\le a_i \\le 10^{9}$\n*   $0 \\le X \\le 10^9$\n*   All input values are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$ $X$\n$a_1$ $a_2$ $\\dots$ $a_N$"},{"iden":"sample input 1","content":"3 1\n0 1 2"},{"iden":"sample output 1","content":"3\n\nWe explain one order where MP never becomes negative.\n\n*   First, light lamp $1$. MP decreases by $0$.\n*   Next, light lamp $3$. MP decreases by $1$.\n*   Finally, light lamp $2$. MP decreases by $0$.\n\nNote that the cost of a lamp never becomes negative."},{"iden":"sample input 2","content":"6 8\n2 1 4 8 1 4"},{"iden":"sample output 2","content":"176"},{"iden":"sample input 3","content":"20 50\n0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19"},{"iden":"sample output 3","content":"63942667\n\nDo not forget to find the remainder modulo $998244353$."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}