{"raw_statement":[{"iden":"problem statement","content":"There are $N$ cells arranged in a row, numbered $1, 2, \\ldots, N$ from left to right.\nTak lives in these cells and is currently on Cell $1$. He is trying to reach Cell $N$ by using the procedure described below.\nYou are given an integer $K$ that is less than or equal to $10$, and $K$ non-intersecting segments $[L_1, R_1], [L_2, R_2], \\ldots, [L_K, R_K]$. Let $S$ be the union of these $K$ segments. Here, the segment $[l, r]$ denotes the set consisting of all integers $i$ that satisfy $l \\leq i \\leq r$.\n\n*   \bWhen you are on Cell $i$, pick an integer $d$ from $S$ and move to Cell $i + d$. You cannot move out of the cells.\n\nTo help Tak, find the number of ways to go to Cell $N$, modulo $998244353$."},{"iden":"constraints","content":"*   $2 \\leq N \\leq 2 \\times 10^5$\n*   $1 \\leq K \\leq \\min(N, 10)$\n*   $1 \\leq L_i \\leq R_i \\leq N$\n*   $[L_i, R_i]$ and $[L_j, R_j]$ do not intersect ($i \\neq j$)\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $K$\n$L_1$ $R_1$\n$L_2$ $R_2$\n$:$\n$L_K$ $R_K$"},{"iden":"sample input 1","content":"5 2\n1 1\n3 4"},{"iden":"sample output 1","content":"4\n\nThe set $S$ is the union of the segment $[1, 1]$ and the segment $[3, 4]$, therefore $S = { 1, 3, 4 }$ holds.\nThere are $4$ possible ways to get to Cell $5$:\n\n*   $1 \\to 2 \\to 3 \\to 4 \\to 5$,\n*   $1 \\to 2 \\to 5$,\n*   $1 \\to 4 \\to 5$ and\n*   $1 \\to 5$."},{"iden":"sample input 2","content":"5 2\n3 3\n5 5"},{"iden":"sample output 2","content":"0\n\nBecause $S = { 3, 5 }$ holds, you cannot reach to Cell $5$. Print $0$."},{"iden":"sample input 3","content":"5 1\n1 2"},{"iden":"sample output 3","content":"5"},{"iden":"sample input 4","content":"60 3\n5 8\n1 3\n10 15"},{"iden":"sample output 4","content":"221823067\n\nNote that you have to print the answer modulo $998244353$."}],"translated_statement":null,"sample_group":[],"show_order":["render_html"],"formal_statement":null,"simple_statement":null,"has_page_source":true}