{"raw_statement":[{"iden":"problem statement","content":"There is a blackboard with a set of positive integers written on it. Initially, the set $S=\\lbrace 1,2,\\dots,A,A+1,A+2,\\dots,A+B\\rbrace$ is written on the blackboard.\nTakahashi wants to perform the following operation $N-1$ times to have $N$ sets on the blackboard:\n\n*   From the sets of integers written on the blackboard, choose a set $S_0$ that contains at least one element not greater than $A$ and at least one element not less than $A+1$. From the chosen set $S_0$, choose one element $a$ not greater than $A$ and one element $b$ not less than $A+1$. Erase the set $S_0$ from the blackboard and write two sets $S_1$ and $S_2$ of his choice that satisfy all of the following conditions:\n    *   The union of $S_1$ and $S_2$ is $S_0$, and they have no common elements.\n    *   $a \\in S_1, b \\in S_2$\n\nFind the number of possible ways to perform the series of operations, modulo $998244353$.\nHere, two series of operations are distinguished when there is an $i\\ (1 \\leq i \\leq N-1)$ such that $S_0$, $a$, $b$, $S_1$, or $S_2$ chosen in the $i$\\-th operation of one series is different from that of the other series."},{"iden":"constraints","content":"*   $2 \\leq N \\leq 2 \\times 10^5$\n*   $1 \\leq A,B \\leq 2 \\times 10^5$\n*   $N \\leq A+B$\n*   All input values are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$ $A$ $B$"},{"iden":"sample input 1","content":"3 2 4"},{"iden":"sample output 1","content":"1728\n\nOne possible series of operations is as follows:\n\n*   Choose $S_0=\\lbrace 1,2,3,4,5,6\\rbrace$, let $a=2$ and $b=5$, and let $S_1 =\\lbrace 1,2,3,6\\rbrace$ and $S_2=\\lbrace 4,5\\rbrace$. There are now two sets of integers written on the blackboard: $\\lbrace 1,2,3,6\\rbrace$ and $\\lbrace 4,5\\rbrace$.\n*   Choose $S_0=\\lbrace 1,2,3,6\\rbrace$, let $a=1$ and $b=3$, and let $S_1 = \\lbrace1,2\\rbrace$ and $S_2=\\lbrace 3,6\\rbrace$. There are now three sets of integers written on the blackboard: $\\lbrace 1,2\\rbrace$, $\\lbrace 3,6\\rbrace$, and $\\lbrace 4,5\\rbrace$."},{"iden":"sample input 2","content":"4 1 3"},{"iden":"sample output 2","content":"6\n\nIf we let $a=1$ and $b=2$ and let $S_1 = \\lbrace 1\\rbrace$ and $S_2 = \\lbrace 2,3,4\\rbrace$ in the first operation, we can no longer perform the second and subsequent operations.\nDo not count these cases where we cannot complete $N-1$ operations."},{"iden":"sample input 3","content":"5 6 6"},{"iden":"sample output 3","content":"84486693"},{"iden":"sample input 4","content":"173173 173173 173173"},{"iden":"sample output 4","content":"446948086"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}