結果
| 問題 |
No.886 Direct
|
| ユーザー |
 uwi
|
| 提出日時 | 2019-09-13 22:00:45 |
| 言語 | Java (openjdk 23) |
| 結果 |
AC
|
| 実行時間 | 1,268 ms / 4,000 ms |
| コード長 | 6,789 bytes |
| コンパイル時間 | 5,167 ms |
| コンパイル使用メモリ | 87,508 KB |
| 実行使用メモリ | 72,632 KB |
| 最終ジャッジ日時 | 2024-07-04 04:15:15 |
| 合計ジャッジ時間 | 18,575 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 32 |
ソースコード
package contest190913;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.util.Map;
public class E {
InputStream is;
PrintWriter out;
String INPUT = "";
void solve()
{
// a, b
// gcd(a, b) = 1
// sum (h-a)*(w-b)*2
// + (h-1)w + w(h-1)
long H = nl(), W = nl();
int mod = 1000000007;
cache = new HashMap<>();
long ab = dfsab(H, W);
cache = new HashMap<>();
long a = dfsa(H, W);
long b = dfsa(W, H);
cache = new HashMap<>();
long C = dfs(H, W);
long ans = (2*H*W%mod*C - 2*W*a - 2*H*b + 2*ab + (H-1)*W + H*(W-1)) % mod;
if(ans < 0)ans += mod;
// tr(a);
// long q = 0;
// long r = 0;
// long s = 0;
// for(int i = 1;i <= H;i++) {
// for(int j = 1;j <= W;j++) {
// if(gcd(i, j) == 1) {
// q += (long)i*j;
// r += (long)i;
// s += 1;
// }
// }
// }
// tr(ab, a, C);
// tr(q%mod, r%mod, s%mod);
out.println(ans);
}
public static int gcd(int a, int b) {
while (b > 0) {
int c = a;
a = b;
b = c % b;
}
return a;
}
int mod = 1000000007;
long dfsab(long H, long W)
{
if(H == 0 || W == 0)return 0;
long code = H<<32|W;
if(cache.containsKey(code))return cache.get(code);
if(H == 1) {
return s1(W, mod);
}
if(W == 1) {
return s1(H, mod);
}
int S = (int)Math.sqrt(Math.max(H, W));
long all = s1(H, mod) * s1(W, mod) % mod;
for(int i = 2;i <= S;i++) {
all -= (long)i*i*dfsab(H/i, W/i);
all %= mod;
}
for(long x = Math.min(H, W), d = H/x, e = W/x;;) {
// H/x = d, W/x = e
long ned = H/(d+1);
long nee = W/(e+1);
long R = Math.max(ned, nee);
R = Math.max(R, S);
// (R, x]
if(R > x)break;
all -= dfsab(d, e) * (s2(x, mod) - s2(R, mod));
// tr(R, x, d, e);
all %= mod;
if(R == S)break;
x = R;
if(ned > nee) {
d++;
}else {
e++;
}
}
if(all < 0)all += mod;
cache.put(code, all);
return all;
}
long dfsa(long H, long W)
{
if(H == 0 || W == 0)return 0;
long code = H<<32|W;
if(cache.containsKey(code))return cache.get(code);
if(H == 1) {
return W;
}
if(W == 1) {
return s1(H, mod);
}
int S = (int)Math.sqrt(Math.max(H, W));
long all = s1(H, mod) * W % mod;
for(int i = 2;i <= S;i++) {
all -= (long)i*dfsa(H/i, W/i);
all %= mod;
}
for(long x = Math.min(H, W), d = H/x, e = W/x;;) {
// H/x = d, W/x = e
long ned = H/(d+1);
long nee = W/(e+1);
long R = Math.max(ned, nee);
R = Math.max(R, S);
if(R > x)break;
// (R, x]
all -= dfsa(d, e) * (s1(x, mod) - s1(R, mod));
all %= mod;
if(R == S)break;
x = R;
if(ned > nee) {
d++;
}else {
e++;
}
}
if(all < 0)all += mod;
cache.put(code, all);
return all;
}
long dfs(long H, long W)
{
if(H == 0 || W == 0)return 0;
long code = H<<32|W;
if(cache.containsKey(code))return cache.get(code);
if(H == 1) {
return W;
}
if(W == 1) {
return H;
}
int S = (int)Math.sqrt(Math.max(H, W));
long all = H * W % mod;
for(int i = 2;i <= S;i++) {
all -= (long)dfs(H/i, W/i);
all %= mod;
}
for(long x = Math.min(H, W), d = H/x, e = W/x;;) {
// H/x = d, W/x = e
long ned = H/(d+1);
long nee = W/(e+1);
long R = Math.max(ned, nee);
R = Math.max(R, S);
if(R > x)break;
// (R, x]
// tr(R, x, d, e);
all -= dfs(d, e) * (x-R);
all %= mod;
if(R == S)break;
x = R;
if(ned > nee) {
d++;
}else {
e++;
}
}
if(all < 0)all += mod;
cache.put(code, all);
return all;
}
public static long s2(long n, int mod)
{
long a = n, b = n+1, c = 2*n+1;
if(a % 2 == 0){
a /= 2;
}else{
b /= 2;
}
if(a % 3 == 0){
a /= 3;
}else if(b % 3 == 0){
b /= 3;
}else{
c /= 3;
}
return (a%mod)*(b%mod)%mod*(c%mod)%mod;
}
Map<Long, Long> cache;
public static long s1(long n, int mod)
{
if(n % 2 == 0){
return (n/2%mod)*((n+1)%mod)%mod;
}else{
return (n%mod)*((n+1)/2%mod)%mod;
}
}
void run() throws Exception
{
is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
out = new PrintWriter(System.out);
long s = System.currentTimeMillis();
solve();
out.flush();
if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
// Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){
// @Override
// public void run() {
// long s = System.currentTimeMillis();
// solve();
// out.flush();
// if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
// }
// };
// t.start();
// t.join();
}
public static void main(String[] args) throws Exception { new E().run(); }
private byte[] inbuf = new byte[1024];
public int lenbuf = 0, ptrbuf = 0;
private int readByte()
{
if(lenbuf == -1)throw new InputMismatchException();
if(ptrbuf >= lenbuf){
ptrbuf = 0;
try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
if(lenbuf <= 0)return -1;
}
return inbuf[ptrbuf++];
}
private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
private double nd() { return Double.parseDouble(ns()); }
private char nc() { return (char)skip(); }
private String ns()
{
int b = skip();
StringBuilder sb = new StringBuilder();
while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
sb.appendCodePoint(b);
b = readByte();
}
return sb.toString();
}
private char[] ns(int n)
{
char[] buf = new char[n];
int b = skip(), p = 0;
while(p < n && !(isSpaceChar(b))){
buf[p++] = (char)b;
b = readByte();
}
return n == p ? buf : Arrays.copyOf(buf, p);
}
private int[] na(int n)
{
int[] a = new int[n];
for(int i = 0;i < n;i++)a[i] = ni();
return a;
}
private long[] nal(int n)
{
long[] a = new long[n];
for(int i = 0;i < n;i++)a[i] = nl();
return a;
}
private char[][] nm(int n, int m) {
char[][] map = new char[n][];
for(int i = 0;i < n;i++)map[i] = ns(m);
return map;
}
private int[][] nmi(int n, int m) {
int[][] map = new int[n][];
for(int i = 0;i < n;i++)map[i] = na(m);
return map;
}
private int ni() { return (int)nl(); }
private long nl()
{
long num = 0;
int b;
boolean minus = false;
while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
if(b == '-'){
minus = true;
b = readByte();
}
while(true){
if(b >= '0' && b <= '9'){
num = num * 10 + (b - '0');
}else{
return minus ? -num : num;
}
b = readByte();
}
}
private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); }
}