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878.java
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878.java
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sample 0 ms submission
//import java.util.HashMap;
class Solution {
public int nthMagicalNumber(int n, int a, int b) {
if (a == b) {
return (int)(((long) a) * n % 1_000_000_007);
}
if (a > b) {
a = b + a;
b = a - b;
a = a - b;
}
long nok = findNok(b, a);
long min = a;
long max = (a + b) * 1_000_000_007L;
while (min != max) {
long middle = (min + max) >> 1;
long iterations = middle / a + middle / b - middle / nok;
if (iterations < n)
min = middle;
else if (iterations > n)
max = middle;
else {
long result = Math.max( (middle / a) * a, (middle / b) * b);
return (int)(result % 1_000_000_007);
}
}
return 0;
}
long findNod(int a, int b) {
if (b == 0)
return a;
else
return findNod(b, a % b);
}
long findNok(int a, int b) {
return (a / findNod(a, b)) * b;
}
};
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sample 31664 kb submission
class Solution {
public int nthMagicalNumber(int N, int A, int B) {
int MOD = 1_000_000_007;
int L = A / gcd(A, B) * B;
int M = L / A + L / B - 1;
int q = N / M, r = N % M;
long ans = (long) q * L % MOD;
if (r == 0)
return (int) ans;
int[] heads = new int[]{A, B};
for (int i = 0; i < r - 1; ++i) {
if (heads[0] <= heads[1])
heads[0] += A;
else
heads[1] += B;
}
ans += Math.min(heads[0], heads[1]);
return (int) (ans % MOD);
}
public int gcd(int x, int y) {
if (x == 0) return y;
return gcd(y % x, x);
}
}
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