Submission #16714

#	Time	Username	Problem	Language	Result	Execution time	Memory
16714		gs14004	Xtreme gcd sum (kriii2_X)	C++14	1 / 4	4000 ms	44688 KiB

X

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <limits.h>
#include <stack>
#include <queue>
#include <map>
#include <set>
#include <algorithm>
#include <string>
#include <functional>
#include <vector>
#include <numeric>
#include <deque>
#include <utility>
#include <bitset>
#include <iostream>
using namespace std;
typedef long long lint;
typedef long double llf;
typedef pair<int, int> pi;

const int mod = 1e9 + 7;
const int maxp = 1e6;

int che[1000005];
int moebius[1000005];
int n;

lint mod_inv(int x, int p){
	lint ret = 1, piv = x;
	while(p){
		if(p&1) ret *= piv;
		piv *= piv;
		ret %= mod;
		piv %= mod;
		p >>= 1;
	}
	return ret;
}

void get_moebius(){
	for(int i=2; i<=maxp; i++){
		for(int j=i; j<=maxp; j+=i){
			if(!che[j]) che[j] = i;
		}
	}
	for(int i=1; i<=maxp; i++){
		int cnt = 0, lst = -1;
		int x = i;
		while(x > 1){
			if(lst == che[x]){
				cnt = -1;
				break;
			}
			lst = che[x];
			x /= lst;
			cnt++;
		}
		if(cnt < 0) continue;
		moebius[i] = cnt % 2 ? -1 : 1;
	}
}

vector<int> change[1000005];
int dx[1000005];
lint cnt[1000005];

int main(){
	scanf("%d",&n);
	fill(cnt, cnt + maxp + 1, 1);
	for(int i=0; i<n; i++){
		int a, b;
		scanf("%d %d",&a, &b);
		int pos = 1, cur = -1;
		int nxt_update = 1;
		while(pos <= maxp){
			cur = b / pos - (a - 1) / pos;
			nxt_update = 1e9;
			int T = b / pos - 1;
			if(T >= 0){
				int s = (b + T + 1) / (T + 1);
				if(s > pos) nxt_update = min(nxt_update, s);
			}
			T = (a - 1) / pos - 1;
			if(T >= 0){
				int s = (a + T) / (T + 1);
				if(s > pos) nxt_update = min(nxt_update, s);
			}
			nxt_update = min(nxt_update, maxp + 1);
			if(cur == 0){
				dx[pos]++;
				dx[nxt_update]--;
			}
			else{
				cnt[nxt_update] *= mod_inv(cur, mod - 2);
				cnt[pos] *= cur;
				cnt[pos] %= mod;
				cnt[nxt_update] %= mod;
			}
			pos = nxt_update;
		}
	}
	for(int i=1; i<=maxp; i++){
		cnt[i] *= cnt[i-1];
		dx[i] += dx[i-1];
		cnt[i] %= mod;
	}
	for(int i=1; i<=maxp; i++){
		if(dx[i]) cnt[i] = 0;
	}
	get_moebius();
	lint ret = 0;
	for(int i=1; i<=maxp; i++){
		for(int j=1; i*j<=maxp; j++){
			ret += 1ll * i * moebius[j] * cnt[i * j] % mod;
			ret %= mod;
		}
	}
	ret += mod;
	ret %= mod;
	printf("%lld",ret);
}

• Subtask 1: 1 / 1
• Subtask 2: 0 / 3