This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#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;
int che[1000005];
int moebius[1000005];
int n, a[10005], b[10005], rng[10005];
lint cnt[1000005];
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;
}
const int maxp = 1e6;
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 main(){
scanf("%d",&n);
fill(cnt, cnt + maxp + 1, 1);
for(int i=0; i<n; i++){
scanf("%d %d",&a[i], &b[i]);
int pos = 1, cur = -1;
int nxt_update = 1;
while(pos <= maxp){
if(nxt_update == pos){
cur = b[i] / pos - (a[i] - 1) / pos;
nxt_update = 1e9;
int T = b[i] / pos - 1;
if(T >= 0){
int s = (b[i] + T + 1) / (T + 1);
if(s > pos) nxt_update = min(nxt_update, s);
}
T = (a[i] - 1) / pos - 1;
if(T >= 0){
int s = (a[i] + T) / (T + 1);
if(s > pos) nxt_update = min(nxt_update, s);
}
}
cnt[pos] *= cur;
cnt[pos] %= mod;
pos++;
}
}
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);
}
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