Unique Strings - NTT

#include<bits/stdc++.h>
using namespace std;


#define endl '\n'
#define ff first
#define ss second
#define pb push_back
// #define int long long
#define sz(v) (int)v.size()
#define inf 2147483647
#define llinf 9223372036854775807
#define all(v) v.begin(),v.end()
#define bp(n) __builtin_popcountll(n)
#define f(i,l,r) for(int i=l;i<=r;i++)
#define rf(i,r,l) for(int i=r;i>=l;i--)
#define fast ios_base::sync_with_stdio(false),cin.tie(NULL),cout.tie(NULL)

const int N = 5e3 + 5, mod = 1e9 + 7, bit = 61;

// Credit : neal

// Be careful about overflow as we are using integer everywhere

template<const int &MOD>
struct _m_int  // This is our new type which will do operations under modulo MOD
{
    int val;   // Value of variable

    _m_int(int64_t v = 0)  // Typecasting into our data type from 64 bit integer
    {
        if (v < 0) v = v % MOD + MOD;
        if (v >= MOD) v %= MOD;
        val = v;
    }

    static int mod_inv(int a, int m = MOD)
    {
        // https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm#Example
        int g = m, r = a, x = 0, y = 1;

        while (r != 0)
        {
            int q = g / r;
            g %= r; swap(g, r);
            x -= q * y; swap(x, y);
        }

        return x < 0 ? x + m : x;
    }

    explicit operator int() const
    {
        return val;
    }

    explicit operator int64_t() const
    {
        return val;
    }

    _m_int& operator += (const _m_int &other)  // Addition
    {
        val -= MOD - other.val;
        if (val < 0) val += MOD;
        return *this;
    }

    _m_int& operator -= (const _m_int &other)  // Subtraction
    {
        val -= other.val;
        if (val < 0) val += MOD;
        return *this;
    }

    static unsigned fast_mod(uint64_t x, unsigned m = MOD) // Mod operation
    {
#if !defined(_WIN32) || defined(_WIN64)
        return x % m;
#endif
        // Optimized mod for Codeforces 32-bit machines.
        // x must be less than 2^32 * m for this to work, so that x / m fits in a 32-bit integer.
        unsigned x_high = x >> 32, x_low = (unsigned) x;
        unsigned quot, rem;
        asm("divl %4\n"
            : "=a" (quot), "=d" (rem)
            : "d" (x_high), "a" (x_low), "r" (m));
        return rem;
    }

    _m_int& operator*=(const _m_int &other)  // Multiplication
    {
        val = fast_mod((uint64_t) val * other.val);
        return *this;
    }

    _m_int& operator/=(const _m_int &other)  // Division
    {
        return *this *= other.inv();
    }

    friend _m_int operator+(const _m_int &a, const _m_int &b) { return _m_int(a) += b; }
    friend _m_int operator-(const _m_int &a, const _m_int &b) { return _m_int(a) -= b; }
    friend _m_int operator*(const _m_int &a, const _m_int &b) { return _m_int(a) *= b; }
    friend _m_int operator/(const _m_int &a, const _m_int &b) { return _m_int(a) /= b; }

    _m_int& operator++()  // Pre-increment
    {
        val = val == MOD - 1 ? 0 : val + 1;
        return *this;
    }

    _m_int& operator--()  // Pre-decrement
    {
        val = val == 0 ? MOD - 1 : val - 1;
        return *this;
    }

    _m_int operator++(int) { _m_int before = *this; ++*this; return before; }  // Post increment
    _m_int operator--(int) { _m_int before = *this; --*this; return before; }  // Post decrement

    _m_int operator-() const  // Change sign
    {
        return val == 0 ? 0 : MOD - val;
    }

    // Boolean operators
    bool operator==(const _m_int &other) const { return val == other.val; }
    bool operator!=(const _m_int &other) const { return val != other.val; }
    bool operator< (const _m_int &other) const { return val <  other.val; }
    bool operator<=(const _m_int &other) const { return val <= other.val; }
    bool operator> (const _m_int &other) const { return val >  other.val; }
    bool operator>=(const _m_int &other) const { return val >= other.val; }

    _m_int inv() const  // Calculating inverse
    {
        return mod_inv(val);
    }

    _m_int pow(int64_t p) const  // Calculating power
    {
        if (p < 0)
            return inv().pow(-p);

        _m_int a = *this, result = 1;

        while (p > 0)
        {
            if (p & 1)
            {
                result *= a;
            }
            a *= a;
            p >>= 1;
        }

        return result;
    }

    friend ostream& operator<<(ostream &os, const _m_int &m)  // Writing output
    {
        return os << m.val;
    }

};

extern const int MOD = 1e9 + 7;
using mod_int = _m_int<MOD>;


template<const int &MOD>
struct NTT
{
    using ntt_int = _m_int<MOD>;

    vector<ntt_int> roots = {0, 1};
    vector<int> bit_reverse;
    int max_size = -1;
    ntt_int root;

    void reset()
    {
        roots = {0, 1};
        max_size = -1;
    }

    static bool is_power_of_two(int n) {  return (n & (n - 1)) == 0;  }

    static int round_up_power_two(int n)
    {
        while (n & (n - 1))
            n = (n | (n - 1)) + 1;

        return max(n, 1);
    }

    // Given n (a power of two), finds k such that n == 1 << k.
    static int get_length(int n)
    {
        assert(is_power_of_two(n));
        return __builtin_ctz(n);
    }

    // Rearranges the indices to be sorted by lowest bit first, then second lowest, etc., rather than highest bit first.
    // This makes even-odd div-conquer much easier.
    void bit_reorder(int n, vector<ntt_int> &values)
    {
        if ((int) bit_reverse.size() != n)
        {
            bit_reverse.assign(n, 0);
            int length = get_length(n);

            for (int i = 1; i < n; i++)
                bit_reverse[i] = (bit_reverse[i >> 1] >> 1) | ((i & 1) << (length - 1));
        }

        for (int i = 0; i < n; i++)
        {
            if (i < bit_reverse[i])
            {
                swap(values[i], values[bit_reverse[i]]);
            }
        }
    }

    void find_root()
    {
        max_size = 1 << __builtin_ctz(MOD - 1);
        root = 2;

        // Find a max_size-th primitive root of MOD.
        while (!(root.pow(max_size) == 1 && root.pow(max_size / 2) != 1))
        {
            root++;
        }
    }

    void prepare_roots(int n)
    {
        if (max_size < 0)
            find_root();

        assert(n <= max_size);

        if ((int) roots.size() >= n)
            return;

        int length = get_length(roots.size());
        roots.resize(n);

        // The roots array is set up such that for a given power of two n >= 2, roots[n / 2] through roots[n - 1] are
        // the first half of the n-th primitive roots of MOD.
        while (1 << length < n)
        {
            // z is a 2^(length + 1)-th primitive root of MOD.
            ntt_int z = root.pow(max_size >> (length + 1));

            for (int i = 1 << (length - 1); i < 1 << length; i++)
            {
                roots[2 * i] = roots[i];
                roots[2 * i + 1] = roots[i] * z;
            }

            length++;
        }
    }

    void fft_iterative(int N, vector<ntt_int> &values)
    {
        assert(is_power_of_two(N));
        prepare_roots(N);
        bit_reorder(N, values);

        for (int n = 1; n < N; n *= 2)
        {
            for (int start = 0; start < N; start += 2 * n)
            {
                for (int i = 0; i < n; i++)
                {
                    ntt_int even = values[start + i];
                    ntt_int odd = values[start + n + i] * roots[n + i];
                    values[start + n + i] = even - odd;
                    values[start + i] = even + odd;
                }
            }
        }
    }

    void invert_fft(int N, vector<ntt_int> &values)
    {
        ntt_int inv_N = ntt_int(N).inv();

        for (int i = 0; i < N; i++)
        {
            values[i] *= inv_N;
        }

        reverse(values.begin() + 1, values.end());
        fft_iterative(N, values);
    }

    const int FFT_CUTOFF = 150;

    // Note: `circular = true` can be used for a 2x speedup when only the `max(n, m) - min(n, m) + 1` fully overlapping
    // ranges are needed. It computes results using indices modulo the power-of-two FFT size; see the brute force below.
    template<typename T>
    vector<T> mod_multiply(const vector<T> &_left, const vector<T> &_right, bool circular = false)
    {
        if (_left.empty() || _right.empty())
            return {};

        vector<ntt_int> left(_left.begin(), _left.end());
        vector<ntt_int> right(_right.begin(), _right.end());

        int n = left.size();
        int m = right.size();

        int output_size = circular ? round_up_power_two(max(n, m)) : n + m - 1;

        // Brute force when either n or m is small enough.
        if (min(n, m) < FFT_CUTOFF)
        {
            auto &&mod_output_size = [&](int x)
            {
                return x < output_size ? x : x - output_size;
            };

            static const uint64_t U64_BOUND = numeric_limits<uint64_t>::max() - (uint64_t) MOD * MOD;
            vector<uint64_t> result(output_size, 0);

            for (int i = 0; i < n; i++)
            {
                for (int j = 0; j < m; j++)
                {
                    int index = mod_output_size(i + j);
                    result[index] += (uint64_t) (int64_t) left[i] * (int64_t) right[j];

                    if (result[index] > U64_BOUND)
                        result[index] %= MOD;
                }
            }
            for (uint64_t &x : result)
                if (x >= MOD)
                    x %= MOD;

            return vector<T>(result.begin(), result.end());
        }

        int N = round_up_power_two(output_size);
        left.resize(N, 0);
        right.resize(N, 0);

        if (left == right)
        {
            fft_iterative(N, left);
            right = left;
        }
        else
        {
            fft_iterative(N, left);
            fft_iterative(N, right);
        }

        for (int i = 0; i < N; i++)
        {
            left[i] *= right[i];
        }

        invert_fft(N, left);
        return vector<T>(left.begin(), left.begin() + output_size);
    }

    template<typename T>
    vector<T> mod_power(const vector<T> &v, int exponent)
    {
        assert(exponent >= 0);
        vector<T> result = {1};

        if (exponent == 0)
            return result;

        for (int k = 31 - __builtin_clz(exponent); k >= 0; k--)
        {
            result = mod_multiply(result, result);

            if (exponent >> k & 1)
                result = mod_multiply(result, v);
        }

        return result;
    }

    template<typename T>
    vector<T> mod_multiply_all(const vector<vector<T>> &polynomials)
    {
        if (polynomials.empty())
            return {1};

        struct compare_size
        {
            bool operator()(const vector<T> &x, const vector<T> &y)
            {
                return x.size() > y.size();
            }
        };

        priority_queue<vector<T>, vector<vector<T>>, compare_size> pq(polynomials.begin(), polynomials.end());

        while (pq.size() > 1)
        {
            vector<T> a = pq.top(); pq.pop();
            vector<T> b = pq.top(); pq.pop();
            pq.push(mod_multiply(a, b));
        }

        return pq.top();
    }
};

NTT<MOD> ntt;

mod_int fact[N], ifact[N];


void pre()
{
    fact[0] = 1;
    int i;
    for (i = 1; i < N; i++)
    {
        fact[i] = (fact[i - 1] * i);
    }
    ifact[N - 1] = fact[N - 1].inv();
    for (i = N - 2; i >= 0; i--)
    {
        ifact[i] = (ifact[i + 1] * (i + 1));
    }
}

signed main()
{
    fast;

    pre();
    string s;
    int mp[26] = {0};
    cin >> s;
    for (auto &x : s)
    {
        mp[x - 'a']++;
    }
    vector<mod_int> res{1};
    f(i, 0, 25)
    {
        if (mp[i] == 0)
        {
            continue;
        }
        vector<mod_int> now;
        f(j, 0, mp[i])
        {
            now.pb(ifact[j]);
        }
        res = ntt.mod_multiply(res, now);
    }
    int n = sz(s);
    n = min(n, sz(res));
    mod_int ans = 0;
    f(i, 1, n)
    {
        ans += (fact[i] * res[i]);
    }
    cout << ans;
    return 0;
}