<p>A positive integer is <em>magical</em> if it is divisible by either <code>a</code> or <code>b</code>.</p>

<p>Given the three integers <code>n</code>, <code>a</code>, and <code>b</code>, return the <code>n<sup>th</sup></code> magical number. Since the answer may be very large, <strong>return it modulo </strong><code>10<sup>9</sup> + 7</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 1, a = 2, b = 3
<strong>Output:</strong> 2
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 4, a = 2, b = 3
<strong>Output:</strong> 6
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 10<sup>9</sup></code></li>
	<li><code>2 &lt;= a, b &lt;= 4 * 10<sup>4</sup></code></li>
</ul>

class Solution {
public:
    int nthMagicalNumber(int n, int a, int b) {
        long long int l=min(a,b);
        long long int h=n*l;
        long long int lcm=a*b/gcd(a,b);
        long long mid,factor;
        while(l<=h){
            mid=(l+h)/2;
            factor=mid/a+mid/b-mid/lcm;
            if(factor<n){
                l=mid+1;
            }
            else{
                h=mid-1;
            }
        }
        long long int mod=1e9+7;
        return l%mod;
    }
    int gcd(int a,int b){
        if(a==0){return b;}
        else{
            return gcd(b%a,a);
        }
    }
};
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