<p>Given two strings s and t, return <i>the number of distinct</i> <b><i>subsequences</i></b><i> of </i>s<i> which equals </i>t.</p>

<p>The test cases are generated so that the answer fits on a 32-bit signed integer.</p>

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

<pre>
<strong>Input:</strong> s = &quot;rabbbit&quot;, t = &quot;rabbit&quot;
<strong>Output:</strong> 3
<strong>Explanation:</strong>
As shown below, there are 3 ways you can generate &quot;rabbit&quot; from s.
<code><strong><u>rabb</u></strong>b<strong><u>it</u></strong></code>
<code><strong><u>ra</u></strong>b<strong><u>bbit</u></strong></code>
<code><strong><u>rab</u></strong>b<strong><u>bit</u></strong></code>
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;babgbag&quot;, t = &quot;bag&quot;
<strong>Output:</strong> 5
<strong>Explanation:</strong>
As shown below, there are 5 ways you can generate &quot;bag&quot; from s.
<code><strong><u>ba</u></strong>b<u><strong>g</strong></u>bag</code>
<code><strong><u>ba</u></strong>bgba<strong><u>g</u></strong></code>
<code><u><strong>b</strong></u>abgb<strong><u>ag</u></strong></code>
<code>ba<u><strong>b</strong></u>gb<u><strong>ag</strong></u></code>
<code>babg<strong><u>bag</u></strong></code></pre>

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

<ul>
	<li><code>1 &lt;= s.length, t.length &lt;= 1000</code></li>
	<li><code>s</code> and <code>t</code> consist of English letters.</li>
</ul>

class Solution
{
public:
    int numDistinct(string s, string t)
    {
        int n = s.size();
        int m = t.size();
        vector<set<tuple<int, unsigned long long, unsigned long long>>> F(m);
        unsigned long long e = 1;
        for (int j = n - 1; j >= 0; --j)
        {
            if (s[j] == t[m - 1])
            {
                F[m - 1].insert({j, 1, e});
                ++e;
            }
        }
        /*
        for (auto x: F[m - 1])
        {
            cout << get<0>(x) << get<1>(x) << get<2>(x) << ' ';
        }
        cout << '\n';
        */
        for (int i = m - 2; i >= 0; --i)
        {
            unsigned long long d = 0;
            for (int j = n - 1; j >= 0; --j)
            {
                if (s[j] == t[i])
                {
                    unsigned long long c = 0;
                    auto p = F[i + 1].lower_bound({j + 1, 0, 0});
                    if (p != F[i + 1].end())
                    {
                        c = get<2>(*p);
                        d += c;
                        F[i].insert({j, c, d});
                    }
                }
            }
        }
        /*
        for (int i = m - 1; i >= 0; --i)
        {
            cout << i << '(' << t[i] << ')' << ' ';
            for (auto x : F[i])
            {
                cout << get<0>(x) << get<1>(x) << get<2>(x) << ' ';
            }
            cout << '\n';
        }
        */
        return get<2>(*(F[0].begin()));
    }
};
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