結果
| 問題 |
No.754 畳み込みの和
|
| コンテスト | |
| ユーザー |
 shun_skycrew
|
| 提出日時 | 2020-09-17 01:16:42 |
| 言語 | Java (openjdk 23) |
| 結果 |
AC
|
| 実行時間 | 1,275 ms / 5,000 ms |
| コード長 | 27,346 bytes |
| コンパイル時間 | 3,944 ms |
| コンパイル使用メモリ | 96,532 KB |
| 実行使用メモリ | 69,532 KB |
| 最終ジャッジ日時 | 2024-06-22 03:53:30 |
| 合計ジャッジ時間 | 9,684 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 3 |
ソースコード
import java.util.*;
import java.io.*;
import java.math.*;
import java.util.function.*;
public class Main implements Runnable {
static boolean DEBUG;
public static void main(String[] args) {
DEBUG = args.length > 0 && args[0].equals("-DEBUG");
Thread.setDefaultUncaughtExceptionHandler((t, e) -> { e.printStackTrace(); System.exit(1); });
new Thread(null, new Main(), "", 1 << 31).start();
}
public void run() {
Solver solver = new Solver();
solver.solve();
solver.exit();
}
static class FastScanner {
private final InputStream in = System.in;
private final byte[] buffer = new byte[1024];
private int pointer = 0;
private int buflen = 0;
private boolean hasNextByte() {
if(pointer < buflen) return true;
else {
pointer = 0;
try {
buflen = in.read(buffer);
}catch (IOException e) {
e.printStackTrace();
}
return buflen > 0;
}
}
private int readByte() { if(hasNextByte()) return buffer[pointer ++]; else return -1; }
private boolean isPrintableChar(int c) { return isPrintableChar(c, false); }
private boolean isPrintableChar(int c, boolean includingSpace) { return (includingSpace ? 32 : 33) <= c && c <= 126; }
private void skipUnprintable() { skipUnprintable(false); }
private void skipUnprintable(boolean includingSpace) { while(hasNextByte() && !isPrintableChar(buffer[pointer], includingSpace)) pointer++; }
private boolean hasNext() { return hasNext(false); }
private boolean hasNext(boolean includingSpace) { skipUnprintable(includingSpace); return hasNextByte(); }
private StringBuilder sb = new StringBuilder();
public String next() { return next(false); }
public String next(boolean includingSpace) {
if(!hasNext(includingSpace)) throw new NoSuchElementException();
sb.setLength(0);
int b = readByte();
while(isPrintableChar(b, includingSpace)) {
sb.appendCodePoint(b);
b = readByte();
}
return sb.toString();
}
public long nextLong() {
if(!hasNext()) throw new NoSuchElementException();
long n = 0;
boolean minus = false;
int b = readByte();
if(b == '-') {
minus = true;
b = readByte();
}
if(b < '0' || '9' < b) throw new NumberFormatException();
while(true) {
if('0' <= b && b <= '9') n = n * 10 + b - '0';
else if(b == -1 || !isPrintableChar(b)) return minus ? -n : n;
else throw new NumberFormatException();
b = readByte();
}
}
}
static class Solver {
FastScanner sc = new FastScanner();
public Solver() { }
String ns() { return ns(false); }
String ns(boolean includingSpace) { return sc.next(includingSpace); }
String[] ns(int n) { return ns(n, false); }
String[] ns(int n, boolean includingSpace) {
String a[] = new String[n];
for(int i = 0; i < n; i ++) a[i] = ns(includingSpace);
return a;
}
String[][] ns(int n, int m) { return ns(n, m, false); }
String[][] ns(int n, int m, boolean includingSpace) {
String a[][] = new String[n][m];
for(int i = 0; i < n; i ++) a[i] = ns(m, includingSpace);
return a;
}
char nc() { return ns().charAt(0); }
char[] nc(int n) {
String str = ns();
if(n < 0) n = str.length();
char a[] = new char[n];
for(int i = 0; i < n; i ++) a[i] = str.charAt(i);
return a;
}
char[][] nc(int n, int m) {
char a[][] = new char[n][m];
for(int i = 0; i < n; i ++) a[i] = nc(m);
return a;
}
boolean[] nb(int n, char t) {
char c[] = nc(-1);
if(n < 0) n = c.length;
boolean a[] = new boolean[n];
for(int i = 0; i < n; i ++) a[i] = c[i] == t;
return a;
}
boolean[][] nb(int n, int m, char t) {
boolean a[][] = new boolean[n][m];
for(int i = 0; i < n; i ++) a[i] = nb(m, t);
return a;
}
int ni() { return Math.toIntExact(sc.nextLong()); }
int[] ni(int n) {
int a[] = new int[n];
for(int i = 0; i < n; i ++) a[i] = ni();
return a;
}
int[][] ni(int n, int m) {
int a[][] = new int[n][m];
for(int i = 0; i < n; i ++) a[i] = ni(m);
return a;
}
long nl() { return sc.nextLong(); }
long[] nl(int n) {
long a[] = new long[n];
for(int i = 0; i < n; i ++) a[i] = nl();
return a;
}
long[][] nl(int n, int m) {
long a[][] = new long[n][m];
for(int i = 0; i < n; i ++) a[i] = nl(m);
return a;
}
double nd() { return Double.parseDouble(sc.next()); }
double[] nd(int n) {
double a[] = new double[n];
for(int i = 0; i < n; i ++) a[i] = nd();
return a;
}
double[][] nd(int n, int m) {
double a[][] = new double[n][m];
for(int i = 0; i < n; i ++) a[i] = nd(m);
return a;
}
String booleanToString(boolean b) { return b ? "#" : "."; }
PrintWriter out = new PrintWriter(System.out);
PrintWriter err = new PrintWriter(System.err);
StringBuilder sb4prtln = new StringBuilder();
void prt() { out.print(""); }
<T> void prt(T a) { out.print(a); }
void prtln() { out.println(""); }
<T> void prtln(T a) { out.println(a); }
void prtln(int... a) {
sb4prtln.setLength(0);
for(int element : a) sb4prtln.append(element+" ");
prtln(sb4prtln.toString().trim());
}
void prtln(long... a) {
sb4prtln.setLength(0);
for(long element : a) sb4prtln.append(element+" ");
prtln(sb4prtln.toString().trim());
}
void prtln(double... a) {
sb4prtln.setLength(0);
for(double element : a) sb4prtln.append(element+" ");
prtln(sb4prtln.toString().trim());
}
void prtln(String... a) {
sb4prtln.setLength(0);
for(String element : a) sb4prtln.append(element+" ");
prtln(sb4prtln.toString().trim());
}
void prtln(char... a) {
sb4prtln.setLength(0);
for(char element : a) sb4prtln.append(element);
prtln(sb4prtln.toString());
}
void prtln(boolean... a) {
sb4prtln.setLength(0);
for(boolean element : a) sb4prtln.append(booleanToString(element));
prtln(sb4prtln.toString());
}
void prtln(int[][] a) { for(int[] element : a) prtln(element); }
void prtln(long[][] a) { for(long[] element : a) prtln(element); }
void prtln(double[][] a) { for(double[] element : a) prtln(element); }
void prtln(String[][] a) { for(String[] element : a) prtln(element); }
void prtln(char[][] a) { for(char[] element : a) prtln(element); }
void prtln(boolean[][] a) { for(boolean[] element : a) prtln(element); }
String errconvert(int a) { return isINF(a) ? "_" : String.valueOf(a); }
String errconvert(long a) { return isINF(a) ? "_" : String.valueOf(a); }
void errprt(int a) { if(DEBUG) err.print(errconvert(a)); }
void errprt(long a) { if(DEBUG) err.print(errconvert(a)); }
void errprt() { if(DEBUG) err.print(""); }
<T> void errprt(T a) { if(DEBUG) err.print(a); }
void errprt(boolean a) { if(DEBUG) errprt(booleanToString(a)); }
void errprtln() { if(DEBUG) err.println(""); }
void errprtln(int a) { if(DEBUG) err.println(errconvert(a)); }
void errprtln(long a) { if(DEBUG) err.println(errconvert(a)); }
<T> void errprtln(T a) { if(DEBUG) err.println(a); }
void errprtln(boolean a) { if(DEBUG) errprtln(booleanToString(a)); }
void errprtln(int... a) {
if(DEBUG) {
sb4prtln.setLength(0);
for(int element : a) sb4prtln.append(errconvert(element)+" ");
errprtln(sb4prtln.toString().trim());
}
}
void errprtln(long... a) {
if(DEBUG) {
sb4prtln.setLength(0);
for(long element : a) sb4prtln.append(errconvert(element)+" ");
errprtln(sb4prtln.toString().trim());
}
}
void errprtln(double... a) {
if(DEBUG) {
sb4prtln.setLength(0);
for(double element : a) sb4prtln.append(element+" ");
errprtln(sb4prtln.toString().trim());
}
}
void errprtln(String... a) {
if(DEBUG) {
sb4prtln.setLength(0);
for(String element : a) sb4prtln.append(element+" ");
errprtln(sb4prtln.toString().trim());
}
}
void errprtln(char... a) {
if(DEBUG) {
sb4prtln.setLength(0);
for(char element : a) sb4prtln.append(element);
errprtln(sb4prtln.toString());
}
}
void errprtln(boolean... a) {
if(DEBUG) {
sb4prtln.setLength(0);
for(boolean element : a) sb4prtln.append(booleanToString(element));
errprtln(sb4prtln.toString());
}
}
void errprtln(Object[] a) { if(DEBUG) for(Object element : a) errprtln(element); }
void errprtln(int[][] a) { if(DEBUG) for(int[] element : a) errprtln(element); }
void errprtln(long[][] a) { if(DEBUG) for(long[] element : a) errprtln(element); }
void errprtln(double[][] a) { if(DEBUG) for(double[] element : a) errprtln(element); }
void errprtln(String[][] a) { if(DEBUG) for(String[] element : a) errprtln(element); }
void errprtln(char[][] a) { if(DEBUG) for(char[] element : a) errprtln(element); }
void errprtln(boolean[][] a) { if(DEBUG) for(boolean[] element : a) errprtln(element); }
void errprtln(Object[][] a) { if(DEBUG) for(Object element : a) { errprtln(element); errprtln(); } }
void reply(boolean b) { prtln(b ? "Yes" : "No"); }
void REPLY(boolean b) { prtln(b ? "YES" : "NO"); }
void flush() { out.flush(); if(DEBUG) err.flush(); }
void assertion(boolean b) { if(!b) { flush(); throw new AssertionError(); } }
void exit() { flush(); System.exit(0); }
<T> void exit(T a) { prtln(a); exit(); }
void exit(int... a) { prtln(a); exit(); }
void exit(long... a) { prtln(a); exit(); }
void exit(double... a) { prtln(a); exit(); }
void exit(String... a) { prtln(a); exit(); }
void exit(char... a) { prtln(a); exit(); }
void exit(boolean... a) { prtln(a); exit(); }
void exit(int[][] a) { prtln(a); exit(); }
void exit(long[][] a) { prtln(a); exit(); }
void exit(double[][] a) { prtln(a); exit(); }
void exit(String[][] a) { prtln(a); exit(); }
void exit(char[][] a) { prtln(a); exit(); }
void exit(boolean[][] a) { prtln(a); exit(); }
final long INF = (long)1e18 + 7;
boolean isPlusINF(long a) { return a > INF / 10; }
boolean isMinusINF(long a) { return isPlusINF(- a); }
boolean isINF(long a) { return isPlusINF(a) || isMinusINF(a); }
final int I_INF = (int)1e9 + 7;
boolean isPlusINF(int a) { return a > I_INF / 10; }
boolean isMinusINF(int a) { return isPlusINF(- a); }
boolean isINF(int a) { return isPlusINF(a) || isMinusINF(a); }
int min(int a, int b) { return Math.min(a, b); }
long min(long a, long b) { return Math.min(a, b); }
double min(double a, double b) { return Math.min(a, b); }
<T extends Comparable<T>> T min(T a, T b) { return a.compareTo(b) <= 0 ? a : b; }
int min(int... x) {
int min = x[0];
for(int val : x) min = min(min, val);
return min;
}
long min(long... x) {
long min = x[0];
for(long val : x) min = min(min, val);
return min;
}
double min(double... x) {
double min = x[0];
for(double val : x) min = min(min, val);
return min;
}
int max(int a, int b) { return Math.max(a, b); }
long max(long a, long b) { return Math.max(a, b); }
double max(double a, double b) { return Math.max(a, b); }
<T extends Comparable<T>> T max(T a, T b) { return a.compareTo(b) >= 0 ? a : b; }
int max(int... x) {
int max = x[0];
for(int val : x) max = max(max, val);
return max;
}
long max(long... x) {
long max = x[0];
for(long val : x) max = max(max, val);
return max;
}
double max(double... x) {
double max = x[0];
for(double val : x) max = max(max, val);
return max;
}
<T extends Comparable<T>> T max(T[] x) {
T max = x[0];
for(T val : x) max = max(max, val);
return max;
}
int max(int[][] a) {
int max = a[0][0];
for(int[] ele : a) max = max(max, max(ele));
return max;
}
long max(long[][] a) {
long max = a[0][0];
for(long[] ele : a) max = max(max, max(ele));
return max;
}
double max(double[][] a) {
double max = a[0][0];
for(double[] ele : a) max = max(max, max(ele));
return max;
}
<T extends Comparable<T>> T max(T[][] a) {
T max = a[0][0];
for(T[] ele : a) max = max(max, max(ele));
return max;
}
long sum(int... a) {
long sum = 0;
for(int element : a) sum += element;
return sum;
}
long sum(long... a) {
long sum = 0;
for(long element : a) sum += element;
return sum;
}
double sum(double... a) {
double sum = 0;
for(double element : a) sum += element;
return sum;
}
long sum(boolean... a) {
long sum = 0;
for(boolean element : a) sum += element ? 1 : 0;
return sum;
}
long[] sums(int[] a) {
long sum[] = new long[a.length + 1];
sum[0] = 0;
for(int i = 0; i < a.length; i ++) sum[i + 1] = sum[i] + a[i];
return sum;
}
long[] sums(long[] a) {
long sum[] = new long[a.length + 1];
sum[0] = 0;
for(int i = 0; i < a.length; i ++) sum[i + 1] = sum[i] + a[i];
return sum;
}
double[] sums(double[] a) {
double sum[] = new double[a.length + 1];
sum[0] = 0;
for(int i = 0; i < a.length; i ++) sum[i + 1] = sum[i] + a[i];
return sum;
}
long[] sums(boolean[] a) {
long sum[] = new long[a.length + 1];
sum[0] = 0;
for(int i = 0; i < a.length; i ++) sum[i + 1] = sum[i] + (a[i] ? 1 : 0);
return sum;
}
long[][] sums(int[][] a) {
long sum[][] = new long[a.length + 1][a[0].length + 1];
fill(sum, 0);
for(int i = 0; i < a.length; i ++) {
for(int j = 0; j < a[i].length; j ++) {
sum[i + 1][j + 1] = sum[i + 1][j] + sum[i][j + 1] - sum[i][j] + a[i][j];
}
}
return sum;
}
long[][] sums(long[][] a) {
long sum[][] = new long[a.length + 1][a[0].length + 1];
fill(sum, 0);
for(int i = 0; i < a.length; i ++) {
for(int j = 0; j < a[i].length; j ++) {
sum[i + 1][j + 1] = sum[i + 1][j] + sum[i][j + 1] - sum[i][j] + a[i][j];
}
}
return sum;
}
double[][] sums(double[][] a) {
double sum[][] = new double[a.length + 1][a[0].length + 1];
fill(sum, 0);
for(int i = 0; i < a.length; i ++) {
for(int j = 0; j < a[i].length; j ++) {
sum[i + 1][j + 1] = sum[i + 1][j] + sum[i][j + 1] - sum[i][j] + a[i][j];
}
}
return sum;
}
long[][] sums(boolean[][] a) {
long sum[][] = new long[a.length + 1][a[0].length + 1];
fill(sum, 0);
for(int i = 0; i < a.length; i ++) {
for(int j = 0; j < a[i].length; j ++) {
sum[i + 1][j + 1] = sum[i + 1][j] + sum[i][j + 1] - sum[i][j] + (a[i][j] ? 1 : 0);
}
}
return sum;
}
int constrain(int x, int l, int r) { return min(max(x, min(l, r)), max(l, r)); }
long constrain(long x, long l, long r) { return min(max(x, min(l, r)), max(l, r)); }
double constrain(double x, double l, double r) { return min(max(x, min(l, r)), max(l, r)); }
int abs(int x) { return x >= 0 ? x : - x; }
long abs(long x) { return x >= 0 ? x : - x; }
double abs(double x) { return x >= 0 ? x : - x; }
int signum(int x) { return x > 0 ? 1 : x < 0 ? -1 : 0; }
int signum(long x) { return x > 0 ? 1 : x < 0 ? -1 : 0; }
int signum(double x) { return x > 0 ? 1 : x < 0 ? -1 : 0; }
long round(double x) { return Math.round(x); }
long floor(double x) { return (long)Math.floor(x); }
int divfloor(int a, int b) { return signum(a) == signum(b) ? a / b : - divceil(abs(a), abs(b)); }
long divfloor(long a, long b) { return signum(a) == signum(b) ? a / b : - divceil(abs(a), abs(b)); }
long ceil(double x) { return (long)Math.ceil(x); }
int divceil(int a, int b) { return a >= 0 && b > 0 ? (a + b - 1) / b
: a < 0 && b < 0 ? divceil(abs(a), abs(b))
: - divfloor(abs(a), abs(b)); }
long divceil(long a, long b) { return a >= 0 && b > 0 ? (a + b - 1) / b
: a < 0 && b < 0 ? divceil(abs(a), abs(b))
: - divfloor(abs(a), abs(b)); }
double sqrt(int x) { return Math.sqrt((double)x); }
double sqrt(long x) { return Math.sqrt((double)x); }
double sqrt(double x) { return Math.sqrt(x); }
long fact(int n) {
long ans = 1;
for(int i = 1; i <= n; i ++) ans = Math.multiplyExact(ans, i);
return ans;
}
double pow(double x, double y) { return Math.pow(x, y); }
long pow(long x, long y) {
long ans = 1;
while(true) {
if(y % 2 != 0) ans = Math.multiplyExact(ans, x);
y /= 2;
if(y <= 0) return ans;
x = Math.multiplyExact(x, x);
}
}
int gcd(int a, int b) {
while(true) {
if(b == 0) return a;
int tmp = a;
a = b;
b = tmp % b;
}
}
long gcd(long a, long b) {
while(true) {
if(b == 0) return a;
long tmp = a;
a = b;
b = tmp % b;
}
}
long lcm(long a, long b) { return a / gcd(a, b) * b; }
int gcd(int... a) {
int gcd = 0;
for(int i = 0; i < a.length; i ++) gcd = gcd(gcd, a[i]);
return gcd;
}
long gcd(long... a) {
long gcd = 0;
for(int i = 0; i < a.length; i ++) gcd = gcd(gcd, a[i]);
return gcd;
}
double random() { return Math.random(); }
int random(int max) { return (int)floor(random() * max); }
long random(long max) { return floor(random() * max); }
double random(double max) { return random() * max; }
int random(int min, int max) { return random(max - min) + min; }
long random(long min, long max) { return random(max - min) + min; }
double random(double min, double max) { return random(max - min) + min; }
boolean isUpper(char a) { return a >= 'A' && a <= 'Z'; }
boolean isLower(char a) { return a >= 'a' && a <= 'z'; }
int upperToInt(char a) { return a - 'A'; }
int lowerToInt(char a) { return a - 'a'; }
int numToInt(char a) { return a - '0'; }
int charToInt(char a) { return a >= 'a' ? lowerToInt(a) : a >= 'A' ? upperToInt(a) : numToInt(a); }
char intToUpper(int a) { return (char)(a + 'A'); }
char intToLower(int a) { return (char)(a + 'a'); }
char intToNum(int a) { return (char)(a + '0'); }
int[] charToInt(char[] a) {
int array[] = new int[a.length];
for(int i = 0; i < a.length; i ++) array[i] = charToInt(a[i]);
return array;
}
int numDigits(long a) { return Long.toString(a).length(); }
long bitFlag(int a) { return 1L << (long)a; }
boolean isFlagged(long x, int a) { return (x & bitFlag(a)) != 0; }
long countString(String str, String a) { return (str.length() - str.replace(a, "").length()) / a.length(); }
long countStringAll(String str, String a) { return str.length() - str.replaceAll(a, "").length(); }
void fill(int[] array, int x) { Arrays.fill(array, x); }
void fill(long[] array, long x) { Arrays.fill(array, x); }
void fill(double[] array, double x) { Arrays.fill(array, x); }
void fill(char[] array, char x) { Arrays.fill(array, x); }
void fill(boolean[] array, boolean x) { Arrays.fill(array, x); }
void fill(int[][] array, int x) { for(int[] a : array) fill(a, x); }
void fill(long[][] array, long x) { for(long[] a : array) fill(a, x); }
void fill(double[][] array, double x) { for(double[] a : array) fill(a, x); }
void fill(char[][] array, char x) { for(char[] a : array) fill(a, x); }
void fill(boolean[][] array, boolean x) { for(boolean[] a : array) fill(a, x); }
void fill(int[][][] array, int x) { for(int[][] a : array) fill(a, x); }
void fill(long[][][] array, long x) { for(long[][] a : array) fill(a, x); }
void fill(double[][][] array, double x) { for(double[][] a : array) fill(a, x); }
void fill(char[][][] array, char x) { for(char[][] a : array) fill(a, x); }
void fill(boolean[][][] array, boolean x) { for(boolean[][] a : array) fill(a, x); }
int[] resize(int[] array, int m, int x) {
int resized[] = new int[m];
for(int i = max(0, - x); i < array.length && i + x < m; i ++) resized[i + x] = array[i];
return resized;
}
long[] resize(long[] array, int m, int x) {
long resized[] = new long[m];
for(int i = max(0, - x); i < array.length && i + x < m; i ++) resized[i + x] = array[i];
return resized;
}
double[] resize(double[] array, int m, int x) {
double resized[] = new double[m];
for(int i = max(0, - x); i < array.length && i + x < m; i ++) resized[i + x] = array[i];
return resized;
}
char[] resize(char[] array, int m, int x) {
char resized[] = new char[m];
for(int i = max(0, - x); i < array.length && i + x < m; i ++) resized[i + x] = array[i];
return resized;
}
boolean[] resize(boolean[] array, int m, int x) {
boolean resized[] = new boolean[m];
for(int i = max(0, - x); i < array.length && i + x < m; i ++) resized[i + x] = array[i];
return resized;
}
Object[] resize(Object[] array, int m, int x) {
Object resized[] = new Object[m];
for(int i = max(0, - x); i < array.length && i + x < m; i ++) resized[i + x] = array[i];
return resized;
}
class PairLL implements Comparable<PairLL> {
long a; long b;
PairLL() { }
PairLL(long a, long b) { this.a = a; this.b = b; }
@Override public String toString() { return "("+a+", "+b+")"; }
@Override public int hashCode() { return Objects.hash(a, b); }
@Override
public boolean equals(Object obj) {
if(this == obj) return true;
if(obj == null) return false;
if(this.getClass() != obj.getClass()) return false;
PairLL that = (PairLL) obj;
if(this.a != that.a || this.b != that.b) return false;
return true;
}
@Override
public int compareTo(PairLL that) {
int c = Long.compare(this.a, that.a);
if(c == 0) c = Long.compare(this.b, that.b);
return c;
}
}
PairLL[] factor(long a) {
List<PairLL> factorList = new ArrayList<>();
for(long i = 2; i * i <= a; i ++) {
if(a % i == 0) {
long cnt = 0;
while(a % i == 0) { a /= i; cnt ++; }
factorList.add(new PairLL(i, cnt));
}
}
if(a > 1) factorList.add(new PairLL(a, 1));
PairLL factor[] = new PairLL[factorList.size()];
for(int i = 0; i < factorList.size(); i ++) factor[i] = factorList.get(i);
Arrays.sort(factor);
return factor;
}
public void solve() {
int num = ni() + 1;
long a[] = nl(num);
long b[] = nl(num);
long ans[] = convolution(a, b, (long)1e9 + 7);
long sum = 0;
for(int i = 0; i < num; i ++) {
sum = mod(sum + ans[i], (long)1e9 + 7);
}
prtln(sum);
}
final long MOD1 = 754974721; // 2^24
final long MOD2 = 167772161; // 2^25
final long MOD3 = 469762049; // 2^26
final long M2M3 = MOD2 * MOD3;
final long M1M3 = MOD1 * MOD3;
final long M1M2 = MOD1 * MOD2;
final long M1M2M3 = MOD1 * MOD2 * MOD3;
final long M1INVM2 = 95869806; // inv(MOD1, MOD2);
final long INV1 = 190329765; // inv(MOD2 * MOD3, MOD1);
final long INV2 = 58587104; // inv(MOD1 * MOD3, MOD2);
final long INV3 = 187290749; // inv(MOD1 * MOD2, MOD3);
long[] convolution(long[] a, long[] b, long mod){
final long M1M2MOD = mod(MOD1 * MOD2, mod);
int n = a.length;
int m = b.length;
if(n == 0 || m == 0) return new long[0];
long f1[] = new Convolution(MOD1).convolution(a, b);
long f2[] = new Convolution(MOD2).convolution(a, b);
long f3[] = new Convolution(MOD3).convolution(a, b);
long f[] = new long[n + m - 1];
for(int i = 0; i < f.length; i ++) {
long v1 = mod((f2[i] - f1[i]) * M1INVM2, MOD2);
long v2 = mod(mod(f3[i] - f1[i] - MOD1 * v1, MOD3) * INV3, MOD3);
f[i] = mod(f1[i] + MOD1 * v1 + M1M2MOD * v2, mod);
}
return f;
}
long[] convolution(long[] a, long[] b) { // O((N+M)log(N+M))
int n = a.length;
int m = b.length;
if(n == 0 || m == 0) return new long[0];
long f1[] = new Convolution(MOD1).convolution(a, b);
long f2[] = new Convolution(MOD2).convolution(a, b);
long f3[] = new Convolution(MOD3).convolution(a, b);
long f[] = new long[n + m - 1];
for(int i = 0; i < n + m - 1; i ++) {
long x = 0;
x += (f1[i] * INV1) % MOD1 * M2M3;
x += (f2[i] * INV2) % MOD2 * M1M3;
x += (f3[i] * INV3) % MOD3 * M1M2;
long diff = f1[i] - mod(x, MOD1);
if(diff < 0) diff += MOD1;
long offset[] = {0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};
x -= offset[(int)(diff % 5)];
f[i] = x;
}
return f;
}
class Convolution { // M=mod
long mod;
long g;
long sumE[];
long sumIE[];
int size = 30;
Convolution(long mod) { // O(logM)
this.mod = mod;
g = primitiveRoot(mod);
sumE = new long[size];
sumIE = new long[size];
prepareSum();
}
long primitiveRoot(long mod) { // O(1) or O(√M)
if(mod == 2) return 1;
if(mod == 167772161) return 3;
if(mod == 469762049) return 3;
if(mod == 754974721) return 11;
if(mod == 998244353) return 3;
PairLL factor[] = factor(mod - 1);
outer: for(long g = 2; ; g ++) {
for(PairLL p : factor) if(pow_m(g, (mod - 1) / p.a, mod) == 1) continue outer;
return g;
}
}
void prepareSum() { // O(logM)
long[] es = new long[size];
long[] ies = new long[size];
int len = Long.numberOfTrailingZeros(mod - 1);
long e = pow_m(g, (mod - 1) >> len, mod);
long ie = pow_m(e, mod - 2, mod);
for(int i = len - 2; i >= 0; i --) {
es[i] = e;
ies[i] = ie;
e = mod(e * e, mod);
ie = mod(ie * ie, mod);
}
long tmpE = 1;
long tmpIE = 1;
for(int i = 0; i < len - 2; i++) {
sumE[i] = mod(es[i] * tmpE, mod);
tmpE = mod(tmpE * ies[i], mod);
sumIE[i] = mod(ies[i] * tmpIE, mod);
tmpIE = mod(tmpIE * es[i], mod);
}
}
void butterfly(long[] a) { // O(NlogN)
int n = a.length;
int h = 0;
while((1L << h) < n) h ++;
for(int ph = 1; ph <= h; ph ++) {
int w = 1 << (ph - 1);
int p = 1 << (h - ph);
long tmp = 1;
for(int s = 0; s < w; s ++) {
int offset = s << (h - ph + 1);
for(int i = 0; i < p; i ++) {
long l = a[i + offset];
long r = mod(a[i + offset + p] * tmp, mod);
a[i + offset] = mod(l + r, mod);
a[i + offset + p] = mod(l - r, mod);
}
int x = Integer.numberOfTrailingZeros(~s);
tmp = mod(tmp * sumE[x], mod);
}
}
}
void butterflyInv(long[] a) { // O(NlogN)
int n = a.length;
int h = 0;
while((1L << h) < n) h ++;
for(int ph = h; ph >= 1; ph --) {
int w = 1 << (ph - 1);
int p = 1 << (h - ph);
long tmp = 1;
for(int s = 0; s < w; s ++) {
int offset = s << (h - ph + 1);
for (int i = 0; i < p; i++) {
long l = a[i + offset];
long r = a[i + offset + p];
a[i + offset] = mod(l + r, mod);
a[i + offset + p] = mod((l - r) * tmp, mod);
}
int x = Integer.numberOfTrailingZeros(~s);
tmp = mod(tmp * sumIE[x], mod);
}
}
}
long[] convolution(long[] a, long[] b) { // O((N+M)log(N+M))
int n = a.length;
int m = b.length;
if (n == 0 || m == 0) return new long[0];
int len = 1;
while(len < n + m - 1) len <<= 1;
long g[] = resize(a, len, 0);
long h[] = resize(b, len, 0);
butterfly(g);
butterfly(h);
long f[] = new long[len];
for(int i = 0; i < len; i ++) f[i] = mod(g[i] * h[i], mod);
butterflyInv(f);
f = resize(f, n + m - 1, 0);
long invLen = inv(len, mod);
for(int i = 0; i < f.length; i ++) f[i] = mod(f[i] * invLen, mod);
return f;
}
}
long mod(long x, long mod) { x %= mod; return x + (x < 0 ? mod : 0); } // O(1)
long pow_m(long x, long y, long mod) { // (logY)
x = mod(x, mod);
long ans = 1;
for(; y > 0; y /= 2) {
if(y % 2 != 0) ans = mod(ans * x, mod);
x = mod(x * x, mod);
}
return ans;
}
long inv(long x, long mod) { return pow_m(x, mod - 2, mod); } // O(logM)
long garner(PairLL[] p, long mod){
PairLL p2[] = new PairLL[p.length + 1];
for(int i = 0; i < p.length; i ++) p2[i] = p[i];
p = p2;
p[p.length - 1] = new PairLL(mod, 0);
long coffs[] = new long[p.length];
fill(coffs, 1);
long constants[] = new long[p.length];
fill(constants, 0);
for(int i = 0; i < p.length - 1; i ++) {
long v = (p[i].b - constants[i]) * inv(coffs[i], p[i].a) % p[i].a;
if(v < 0) v += p[i].a;
for(int j = i + 1; j < p.length; j++) {
constants[j] += coffs[j] * v;
constants[j] %= p[j].a;
coffs[j] *= p[i].a;
coffs[j] %= p[j].a;
}
}
return constants[p.length - 1];
}
}
}