{"raw_statement":[{"iden":"problem statement","content":"Takahashi has a playlist with $N$ songs. Song $i$ $(1 \\leq i \\leq N)$ lasts $T_i$ seconds.  \nTakahashi has started random play of the playlist at time $0$.\nRandom play repeats the following: choose one song from the $N$ songs with equal probability and play that song to the end. Here, songs are played continuously: once a song ends, the next chosen song starts immediately. The same song can be chosen consecutively.\nFind the probability that song $1$ is being played $(X + 0.5)$ seconds after time $0$, modulo $998244353$.\nHow to print a probability modulo $998244353$It can be proved that the probability to be found in this problem is always a rational number. Also, the constraints of this problem guarantee that when the probability to be found is expressed as an irreducible fraction $\\frac{y}{x}$, $x$ is not divisible by $998244353$.\nThen, there is a unique integer $z$ between $0$ and $998244352$, inclusive, such that $xz \\equiv y \\pmod{998244353}$. Report this $z$."},{"iden":"constraints","content":"*   $2 \\leq N\\leq 10^3$\n*   $0 \\leq X\\leq 10^4$\n*   $1 \\leq T_i\\leq 10^4$\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$T_1$ $T_2$ $\\ldots$ $T_N$"},{"iden":"sample input 1","content":"3 6\n3 5 6"},{"iden":"sample output 1","content":"369720131\n\nSong $1$ will be playing $6.5$ seconds after time $0$ if songs are played in one of the following orders.\n\n*   Song $1$ $\\to$ Song $1$ $\\to$ Song $1$\n*   Song $2$ $\\to$ Song $1$\n*   Song $3$ $\\to$ Song $1$\n\nThe probability that one of these occurs is $\\frac{7}{27}$.  \nWe have $369720131\\times 27\\equiv 7 \\pmod{998244353}$, so you should print $369720131$."},{"iden":"sample input 2","content":"5 0\n1 2 1 2 1"},{"iden":"sample output 2","content":"598946612\n\n$0.5$ seconds after time $0$, the first song to be played is still playing, so the sought probability is $\\frac{1}{5}$.  \nNote that different songs may have the same length."},{"iden":"sample input 3","content":"5 10000\n1 2 3 4 5"},{"iden":"sample output 3","content":"586965467"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}