/**
 * code generated by JHelper
 * More info: https://github.com/AlexeyDmitriev/JHelper
 * @author Egor Kulikov
 */





#include <bits/stdc++.h>

using namespace std;

#define all(v) (v).begin(), (v).end()

using ll = long long;
using ull = unsigned long long;
using li = __int128;
using uli = unsigned __int128;
using ld = long double;
using pii = pair<int, int>;
using vi = vector<int>;

void doReplace() {
}

template <typename T, typename U, typename...Vs>
void doReplace(T& t, const U& u, Vs&& ...vs) {
    t = u;
    doReplace(vs...);
}

template <typename T, typename...Us>
T minim(T& was, const T& cand, Us&& ...us) {
    if (was > cand) {
        was = cand;
        doReplace(us...);
    }
    return was;
}

template <typename T, typename...Us>
T maxim(T& was, const T& cand, Us&& ...us) {
    if (was < cand) {
        was = cand;
        doReplace(us...);
    }
    return was;
}


template <typename D>
D dPower(D base, ll exponent) {
    if (exponent < 0) {
        return dPower(1 / base, -exponent);
    }
    if (exponent == 0) {
        return 1;
    }
    if ((exponent & 1) == 1) {
        return dPower(base, exponent - 1) * base;
    } else {
        D res = dPower(base, exponent >> 1);
        return res * res;
    }
}


class NumberIterator : iterator<forward_iterator_tag, int> {
public:
    int v;

    NumberIterator(int v) : v(v) {}

    operator int&() { return v; }

    int operator*() { return v; }
};

class range : pii {
public:
    range(int begin, int end) : pii(begin, max(begin, end)) {}

    range(int n) : pii(0, max(0, n)) {}

    NumberIterator begin() {
        return first;
    }

    NumberIterator end() {
        return second;
    }
};


template <typename T>
class arr {
    T* b;
    int n;

    void allocate(int sz) {
#ifdef LOCAL
        if (sz < 0) {
            throw "bad alloc";
        }
#endif
        n = sz;
        if (sz > 0) {
            b = (T*) (::operator new(sz * sizeof(T)));
        } else {
            b = nullptr;
        }
    }

public:
    arr(int n = 0) {
        allocate(n);
#ifdef LOCAL
        view();
#endif
    }

    arr(int n, const T& init) {
        allocate(n);
        for (int i : range(n)) {
            ::new((void*) (b + i)) T(init);
        }
#ifdef LOCAL
        view();
#endif
    }

    arr(initializer_list<T> l) : arr(l.size()) {
        if (n > 0) {
            memcpy(b, l.begin(), n * sizeof(T));
        }
    }

    arr(T* b, int n) : arr(b, b + n) {}

    arr(T* b, T* e) : b(b), n(e - b) {}

    int size() const {
        return n;
    }

    T* begin() {
        return b;
    }

    const T* begin() const {
        return b;
    }

    T* end() {
        return b + n;
    }

    const T* end() const {
        return b + n;
    }

    arr<T> clone() const {
        arr<T> res(n);
        copy(b, b + n, res.begin());
        return res;
    }

    T& operator[](int at) {
#ifdef LOCAL
        if (at < 0 || at >= n) {
            throw "Out of bounds";
        }
#endif
        return b[at];
    }

    const T& operator[](int at) const {
#ifdef LOCAL
        if (at < 0 || at >= n) {
            throw "Out of bounds";
        }
#endif
        return b[at];
    }

    bool operator==(const arr& other) const {
        if (n != other.n) {
            return false;
        }
        for (int i : range(n)) {
            if (b[i] != other.b[i]) {
                return false;
            }
        }
        return true;
    }

    vector<T> view() {
        return vector<T>(b, b + min(n, 50));
    }
};

typedef arr<int> arri;

void decreaseByOne() {}

template <typename T, class...Vs>
void decreaseByOne(arr<T>& array, Vs& ...vs) {
    int n = array.size();
    for (int i : range(n)) {
        array[i]--;
    }
    decreaseByOne(vs...);
}

template <typename T, typename U>
void decreaseByOne(arr<pair<T, U>>& v) {
    for (auto& p : v) {
        p.first--;
        p.second--;
    }
}


template <typename T>
class arr2d {
    T* b;
    int d1;
    int d2;
    int sz;

    void allocate(int n) {
#ifdef LOCAL
        if (n < 0) {
            throw "bad alloc";
        }
#endif
        if (n > 0) {
            b = (T*) (::operator new(n * sizeof(T)));
        } else {
            b = nullptr;
        }
    }

public:
    arr2d(int d1 = 0, int d2 = 0) : d1(d1), d2(d2), sz(d1 * d2) {
#ifdef LOCAL
        if (d1 < 0 || d2 < 0) {
            throw "bad alloc";
        }
#endif
        allocate(sz);
#ifdef LOCAL
        view();
#endif
    }

    arr2d(int d1, int d2, const T& init) : d1(d1), d2(d2), sz(d1 * d2) {
#ifdef LOCAL
        if (d1 < 0 || d2 < 0) {
            throw "bad alloc";
        }
#endif
        allocate(sz);
        for (int i : range(sz)) {
            ::new((void*) (b + i)) T(init);
        }
#ifdef LOCAL
        view();
#endif
    }

    arr2d(T* b, int d1, int d2) : b(b), d1(d1), d2(d2), sz(d1 * d2) {}

    int size() const {
        return sz;
    }

    int dim1() const {
        return d1;
    }

    int dim2() const {
        return d2;
    }

    T* begin() {
        return b;
    }

    T* end() {
        return b + sz;
    }

    T& operator()(int i1, int i2) {
#ifdef LOCAL
        if (i1 < 0 || i1 >= d1 || i2 < 0 || i2 >= d2) {
            throw "Out of bounds";
        }
#endif
        return b[i1 * d2 + i2];
    }

    const T& operator()(int i1, int i2) const {
#ifdef LOCAL
        if (i1 < 0 || i1 >= d1 || i2 < 0 || i2 >= d2) {
            throw "Out of bounds";
        }
#endif
        return b[i1 * d2 + i2];
    }

    T& operator[](const pii& p) {
        return operator()(p.first, p.second);
    }

    const T& operator[](const pii& p) const {
        return operator()(p.first, p.second);
    }

    arr<T> operator[](int at) {
#ifdef LOCAL
        if (at < 0 || at >= d1) {
            throw "Out of bounds";
        }
#endif
        return arr<T>(b + at * d2, d2);
    }

    vector<vector<T>> view() {
        vector<vector<T>> res(min(d1, 50));
        for (int i : range(res.size())) {
            res[i] = (*this)[i].view();
        }
        return res;
    }

    arr2d<T> clone() {
        arr2d<T> res(d1, d2);
        copy(b, b + sz, res.b);
        return res;
    }
};


inline bool isWhitespace(int c) {
    return isspace(c) || c == EOF;
}

class Input {
private:
    bool exhausted = false;
    int bufSize = 4096;
    char* buf = new char[bufSize];
    int bufRead = 0;
    int bufAt = 0;

public:
    inline int get() {
        if (exhausted) {
#ifdef LOCAL
            throw "Input exhausted";
#endif
            return EOF;
        }
        if (bufRead == bufAt) {
            bufRead = fread(buf, sizeof(char), bufSize, stdin);
            bufAt = 0;
        }
        if (bufRead == bufAt) {
            exhausted = true;
            return EOF;
        }
        return buf[bufAt++];
    }

    inline int peek() {
        if (exhausted) {
#ifdef LOCAL
            throw "Input exhausted";
#endif
            return EOF;
        }
        if (bufRead == bufAt) {
            bufRead = fread(buf, sizeof(char), bufSize, stdin);
            bufAt = 0;
        }
        if (bufRead == bufAt) {
            exhausted = true;
            return EOF;
        }
        return buf[bufAt];
    }

private:
    template <typename T>
    inline T readInteger() {
        int c = skipWhitespace();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = get();
        }
        T res = 0;
        do {
            if (!isdigit(c)) {
#ifdef LOCAL
                throw "Number format error";
#endif
                return sgn * res;
            }
            res *= 10;
            res += c - '0';
            c = get();
        } while (!isWhitespace(c));
        return res * sgn;
    }

    void initArrays(int) {}

    template <typename T, class...Vs>
    void initArrays(int n, arr<T>& array, Vs& ...vs) {
        array = arr<T>(n, T());
        initArrays(n, vs...);
    }

    template <typename T, class...Vs>
    void initArrays(int n, vector<T>&, Vs& ...vs) {
        initArrays(n, vs...);
    }

    void readImpl(int) {}

    template <typename T, class...Vs>
    void readImpl(int i, arr<T>& arr, Vs& ...vs) {
        arr[i] = readType<T>();
        readImpl(i, vs...);
    }

    template <typename T, class...Vs>
    void readImpl(int i, vector<T>& arr, Vs& ...vs) {
        arr.push_back(readType<T>());
        readImpl(i, vs...);
    }

public:
    inline int skipWhitespace() {
        int c;
        while (isWhitespace(c = get()) && c != EOF);
        return c;
    }

    inline int peekNext() {
        while (isWhitespace(peek()) && peek() != EOF) {
            get();
        }
        return peek();
    }

    inline int readInt() {
        return readInteger<int>();
    }

    inline ll readLong() {
        return readInteger<ll>();
    }

    inline unsigned readUnsigned() {
        return readInteger<unsigned>();
    }

    string readString() {
        int c = skipWhitespace();
        if (c == EOF) {
#ifdef LOCAL
            throw "Input exhausted";
#endif
            return "";
        }
        string res;
        do {
            res.push_back(c);
        } while (!isWhitespace(c = get()));
        return res;
    }

    arri readIntArray(int size) {
        return readArray<int>(size);
    }

    arr<ll> readLongArray(int size) {
        return readArray<ll>(size);
    }

    arr<double> readDoubleArray(int size) {
        return readArray<double>(size);
    }

    arr<string> readStringArray(int size) {
        return readArray<string>(size);
    }

    arr<char> readCharArray(int size) {
        return readArray<char>(size);
    }

    template <typename T>
    T readType() {
        throw "Operation not supported";
    }

    template <typename U, typename V>
    pair<U, V> readType() {
        U first = readType<U>();
        V second = readType<V>();
        return make_pair(first, second);
    }

    template <typename T>
    arr<T> readArray(int n) {
        arr<T> res(n, T());
        for (int i : range(n)) {
            res[i] = readType<T>();
        }
        return res;
    }


    template <class...Vs>
    void readArrays(int n, Vs& ...vs) {
        initArrays(n, vs...);
        for (int i : range(n)) {
            readImpl(i, vs...);
        }
    }

    template <typename U, typename V>
    arr<pair<U, V>> readArray(int n) {
        arr<pair<U, V>> res(n);
        for (int i : range(n)) {
            res[i] = readType<U, V>();
        }
        return res;
    }

    template <typename T>
    arr2d<T> readTable(int rows, int cols) {
        arr2d<T> result(rows, cols);
        for (int i : range(rows)) {
            for (int j : range(cols)) {
                result(i, j) = readType<T>();
            }
        }
        return result;
    }

    arr2d<int> readIntTable(int rows, int cols) {
        return readTable<int>(rows, cols);
    }

    arr2d<char> readCharTable(int rows, int cols) {
        return readTable<char>(rows, cols);
    }

    string readLine() {
        int c = get();
        if (c == EOF) {
#ifdef LOCAL
            throw "Input exhausted";
#endif
            return "";
        }
        string res;
        do {
            res.push_back(c);
            c = get();
        } while (c != '\n' && c != '\r' && c != EOF);
        return res;
    }

    inline double readDouble() {
        int c = skipWhitespace();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = get();
        }
        double res = 0;
        do {
            if (tolower(c) == 'e') {
                return sgn * res * dPower(double(10), readInt());
            }
            if (!isdigit(c)) {
#ifdef LOCAL
                throw "Number format error";
#endif
                return sgn * res;
            }
            res *= 10;
            res += c - '0';
            c = get();
        } while (!isWhitespace(c) && c != '.');
        if (c == '.') {
            double add = 0;
            int length = 0;
            c = get();
            do {
                if (tolower(c) == 'e') {
                    return sgn * (res + add * dPower(double(10), -length)) * dPower(double(10), readInt());
                }
                if (!isdigit(c)) {
#ifdef LOCAL
                    throw "Number format error";
#endif
                    res += add * dPower(10, -length);
                    return res * sgn;
                }
                add *= 10;
                add += c - '0';
                length++;
                c = get();
            } while (!isWhitespace(c));
            res += add * dPower(double(10), -length);
        }
        return res * sgn;
    }

    inline char readChar() {
        int c = skipWhitespace();
        if (c == EOF) {
#ifdef LOCAL
            throw "Input exhausted";
#endif
            return 0;
        }
        return c;
    }

    inline bool isExhausted() { return exhausted; }

    inline void setBufSize(int newBufSize) {
        if (newBufSize > bufSize) {
            char* newBuf = new char[newBufSize];
            memcpy(newBuf, buf, bufSize);
            buf = newBuf;
        }
        bufSize = newBufSize;
    }
};

template <>
inline double Input::readType() {
    return readDouble();
}

template <>
inline int Input::readType() {
    return readInt();
}

template <>
inline ll Input::readType() {
    return readLong();
}

template <>
inline unsigned Input::readType() {
    return readUnsigned();
}

template <>
inline char Input::readType() {
    return readChar();
}

template <>
inline string Input::readType() {
    return readString();
}

Input in;


class Output {
private:
    ostream* out;

    template <typename T>
    inline void printSingle(const T& value) {
        *out << value;
    }

    template <typename T>
    void printSingle(const vector<T>& array) {
        size_t n = array.size();
        for (int i : range(n)) {
            *out << array[i];
            if (i + 1 != n) {
                *out << ' ';
            }
        }
    }

    template <typename T>
    void printSingle(const arr<T>& array) {
        int n = array.size();
        for (int i : range(n)) {
            *out << array[i];
            if (i + 1 != n) {
                *out << ' ';
            }
        }
    }

    template <typename T>
    void printSingle(const arr2d<T>& array) {
        size_t n = array.dim1();
        size_t m = array.dim2();
        for (int i : range(n)) {
            for (int j : range(m)) {
                *out << array(i, j);
                if (j + 1 != m) {
                    *out << ' ';
                }
            }
            if (i + 1 != n) {
                *out << '\n';
            }
        }
    }

    template <typename T, typename U>
    inline void printSingle(const pair<T, U>& value) {
        *out << value.first << ' ' << value.second;
    }

public:
    bool autoflush;

    Output(ostream& out, bool autoflush) : out(&out), autoflush(autoflush) {
        setPrecision(20);
    }

    void setOut(ostream& nOut) {
        out = &nOut;
        setPrecision(20);
    }

    inline void print() {}

    template <typename T, typename...Targs>
    inline void print(const T& first, const Targs... args) {
        printSingle(first);
        if (sizeof...(args) != 0) {
            *out << ' ';
            print(args...);
        }
        if (autoflush) {
            flush();
        }
    }

    template <typename...Targs>
    inline void printLine(const Targs... args) {
        print(args...);
        *out << '\n';
        if (autoflush) {
            flush();
        }
    }

    inline void flush() {
        out->flush();
    }

    inline void setPrecision(int digs) {
        *out << fixed << setprecision(digs);
    }
};

Output out(cout, false);
Output err(cerr, true);


class ReverseNumberIterator : public NumberIterator {
public:
    ReverseNumberIterator(int v) : NumberIterator(v) {}

    ReverseNumberIterator& operator++() {
        --v;
        return *this;
    }
};

class RevRange : pii {
public:
    RevRange(int begin, int end) : pii(begin - 1, min(begin, end) - 1) {}

    RevRange(int n) : pii(n - 1, min(n, 0) - 1) {}

    ReverseNumberIterator begin() {
        return first;
    }

    ReverseNumberIterator end() {
        return second;
    }
};


const int MOD7 = 1000000007;
const int MOD9 = 1000000009;
const int MODF = 998244353;

int mod = MOD7;

ll gcd(ll a, ll b, ll& x, ll& y) {
    if (a == 0) {
        x = 0;
        y = 1;
        return b;
    }
    int d = gcd(b % a, a, y, x);
    x -= (b / a) * y;
    return d;
}

class modint {
public:
    int n;

    modint() : n(0) {}

    modint(ll n, bool special = false) {
        if (special) {
            this->n = -1;
            return;
        }
        if (n >= 0 && n < mod) {
            this->n = n;
            return;
        }
        n %= mod;
        if (n < 0) {
            n += mod;
        }
        this->n = n;
    }

    modint& operator+=(const modint& other) {
#ifdef LOCAL
        if (n == -1 || other.n == -1) {
            throw "Illegal state";
        }
#endif
        n += other.n;
        if (n >= mod) {
            n -= mod;
        }
        return *this;
    }

    modint& operator-=(const modint& other) {
#ifdef LOCAL
        if (n == -1 || other.n == -1) {
            throw "Illegal state";
        }
#endif
        n -= other.n;
        if (n < 0) {
            n += mod;
        }
        return *this;
    }

    modint& operator*=(const modint& other) {
#ifdef LOCAL
        if (n == -1 || other.n == -1) {
            throw "Illegal state";
        }
#endif
        n = ll(n) * other.n % mod;
        return *this;
    }

    modint& operator/=(const modint& other) {
#ifdef LOCAL
        if (other.n == 0) {
            throw "Division by zero";
        }
        if (n == -1 || other.n == -1) {
            throw "Illegal state";
        }
#endif
        return *this *= other.inverse();
    }

    modint operator-() {
#ifdef LOCAL
        if (n == -1) {
            throw "Illegal state";
        }
#endif
        if (n == 0) {
            return 0;
        }
        return modint(mod - n);
    }

    modint inverse() const {
#ifdef LOCAL
        if (n == -1) {
            throw "Illegal state";
        }
#endif
        ll x, y;
        ll g = gcd(ll(n), ll(mod), x, y);
#ifdef LOCAL
        if (g != 1) {
            throw "not inversable";
        }
#endif
        return x;
    }

    int log(modint alpha);
};

modint nullModint(-1, true);

modint operator+(const modint& a, const modint& b) {
    return modint(a) += b;
}

modint operator-(const modint& a, const modint& b) {
    return modint(a) -= b;
}

modint operator*(const modint& a, const modint& b) {
    return modint(a) *= b;
}

modint operator/(const modint& a, const modint& b) {
    return modint(a) /= b;
}

ostream& operator<<(ostream& out, const modint& val) {
    return out << val.n;
}

bool operator==(const modint& a, const modint& b) {
    return a.n == b.n;
}

bool operator!=(const modint& a, const modint& b) {
    return a.n != b.n;
}

namespace std {
    template <>
    struct hash<modint> {
        size_t operator()(const modint& n) const {
            return n.n;
        }
    };
}

int modint::log(modint alpha) {
#ifdef LOCAL
    if (n == -1 || alpha.n == -1) {
        throw "Illegal state";
    }
#endif
    unordered_map<modint, int> base;
    int exp = 0;
    modint pow = 1;
    modint inv = *this;
    modint alInv = alpha.inverse();
    while (exp * exp < mod) {
        if (inv == 1) {
            return exp;
        }
        base[inv] = exp++;
        pow *= alpha;
        inv *= alInv;
    }
    modint step = pow;
    for (int i = 1;; i++) {
        if (base.count(pow)) {
            return exp * i + base[pow];
        }
        pow *= step;
    }
}


template <typename T>
class arr3d {
    T* b;
    int d1;
    int d2;
    int d3;
    int shift;
    int sz;

    void allocate(int n) {
#ifdef LOCAL
        if (n < 0) {
            throw "bad alloc";
        }
#endif
        if (n > 0) {
            b = (T*) (::operator new(n * sizeof(T)));
        } else {
            b = nullptr;
        }
    }

public:
    arr3d(int d1 = 0, int d2 = 0, int d3 = 0) : d1(d1), d2(d2), d3(d3), shift(d2 * d3), sz(d1 * d2 * d3) {
#ifdef LOCAL
        if (d1 < 0 || d2 < 0 || d3 < 0) {
            throw "bad alloc";
        }
#endif
        allocate(sz);
        for (int i : range(sz)) {
            ::new((void*) (b + i)) T;
        }
#ifdef LOCAL
        view();
#endif
    }

    arr3d(int d1, int d2, int d3, const T& init) : d1(d1), d2(d2), d3(d3), shift(d2 * d3), sz(d1 * d2 * d3) {
#ifdef LOCAL
        if (d1 < 0 || d2 < 0 || d3 < 0) {
            throw "bad alloc";
        }
#endif
        allocate(sz);
        for (int i : range(sz)) {
            ::new((void*) (b + i)) T(init);
        }
#ifdef LOCAL
        view();
#endif
    }

    arr3d(T* b, int d1, int d2, int d3) : b(b), d1(d1), d2(d2), d3(d3), shift(d2 * d3), sz(d1 * d2 * d3) {}

    int size() const {
        return sz;
    }

    int dim1() const {
        return d1;
    }

    int dim2() const {
        return d2;
    }

    int dim3() const {
        return d3;
    }

    T* begin() {
        return b;
    }

    T* end() {
        return b + sz;
    }

    T& operator()(int i1, int i2, int i3) {
#ifdef LOCAL
        if (i1 < 0 || i1 >= d1 || i2 < 0 || i2 >= d2 || i3 < 0 || i3 >= d3) {
            throw "Out of bounds";
        }
#endif
        return b[i1 * shift + i2 * d3 + i3];
    }

    const T& operator()(int i1, int i2, int i3) const {
#ifdef LOCAL
        if (i1 < 0 || i1 >= d1 || i2 < 0 || i2 >= d2 || i3 < 0 || i3 >= d3) {
            throw "Out of bounds";
        }
#endif
        return b[i1 * shift + i2 * d3 + i3];
    }

    arr2d<T> operator[](int at) {
#ifdef LOCAL
        if (at < 0 || at >= d1) {
            throw "Out of bounds";
        }
#endif
        return arr2d<T>(b + at * shift, d2, d3);
    }

    vector<vector<vector<T>>> view() {
        vector<vector<vector<T>>> res(min(d1, 50));
        for (int i = 0; i < res.size(); ++i) {
            res[i] = (*this)[i].view();
        }
        return res;
    }
};


template <typename T>
T gcd(T a, T b) {
    a = abs(a);
    b = abs(b);
    while (b != 0) {
        a = a % b;
        swap(a, b);
    }
    return a;
}

template <typename T>
T lcm(T a, T b) {
    return a / gcd(a, b) * b;
}

template <typename T>
T power(const T& a, ll b) {
    if (b == 0) {
        return 1;
    }
    if ((b & 1) == 0) {
        T res = power(a, b >> 1);
        return res * res;
    } else {
        return power(a, b - 1) * a;
    }
}

template <typename T>
T factorial(int n) {
    T result = 1;
    for (int i = 2; i <= n; i++) {
        result *= i;
    }
    return result;
}

template <typename T>
arr<T> factorials(int length) {
    arr<T> result(length);
    if (length > 0) {
        result[0] = 1;
    }
    for (int i = 1; i < length; i++) {
        result[i] = result[i - 1] * i;
    }
    return result;
}

template <typename T>
arr<T> powers(T base, int length) {
    arr<T> result(length);
    if (length > 0) {
        result[0] = 1;
    }
    for (int i = 1; i < length; i++) {
        result[i] = result[i - 1] * base;
    }
    return result;
}


arr<modint> inverses(int length) {
    arr<modint> result(length);
    if (length > 1) {
        result[1] = 1;
    }
    for (int i = 2; i < length; i++) {
        result[i] = -(mod / i) * result[mod % i];
    }
    return result;
}

arr<modint> inverseFactorials(int length) {
    auto result = inverses(length);
    if (length > 0) {
        result[0] = 1;
    }
    for (int i = 1; i < length; i++) {
        result[i] *= result[i - 1];
    }
    return result;
}

class Combinations {
private:
    arr<modint> fact;
    arr<modint> invFactorial;

public:
    Combinations(int length) {
        fact = factorials<modint>(length);
        invFactorial = inverseFactorials(length);
    }

public:
    modint c(int n, int k) const {
        if (k < 0 || k > n) {
            return 0;
        }
        return fact[n] * invFactorial[k] * invFactorial[n - k];
    }

    modint operator()(int n, int k) const {
        return c(n, k);
    }

    modint factorial(int n) const {
        return fact[n];
    }

    modint inverseFactorial(int n) const {
        return invFactorial[n];
    }
};

arr<modint> bernoulli(int length, Combinations* c = nullptr) {
    arr<modint> b(length);
    if (c == nullptr) {
        c = new Combinations(length + 1);
    }
    if (length > 0) {
        b[0] = 1;
    }
    for (int i : range(1, length)) {
        b[i] = 0;
        for (int j : range(1, i + 1)) {
            b[i] += (*c)(i + 1, j + 1) * b[i - j];
        }
        b[i] = -b[i];
        b[i] /= i + 1;
    }
    return b;
}


class DSecretPassage {
public:
    void solve() {
        auto s = in.readString();

        mod = MODF;
        int zeroes = count(all(s), '0');
        int ones = s.size() - zeroes;
        arri nonFreeZ(s.size() + 1);
        arri nonFreeO(s.size() + 1);
        nonFreeZ[0] = zeroes;
        nonFreeO[0] = ones;
        for (int i : range(s.size())) {
            nonFreeZ[i + 1] = nonFreeZ[i] - (s[i] == '0' ? 1 : 0);
            nonFreeO[i + 1] = nonFreeO[i] - (s[i] == '0' ? 0 : 1);
        }
        arr2d<int> minSuf(zeroes + 1, ones + 1, s.size() + 1);
        minSuf(zeroes, ones) = s.size();
        for (int i : RevRange(zeroes + 1)) {
            for (int j : RevRange(ones + 1)) {
                if (minSuf(i, j) > s.size()) {
                    continue;
                }
                if (minSuf(i, j) == 1) {
                    minSuf(i, j) = 0;
                }
                if (minSuf(i, j) > 1) {
                    int ss = minSuf(i, j);
                    if (s[s.size() - ss] != s[s.size() - ss + 1]) {
                        minim(minSuf(i - 1, j), ss - 2);
                        minim(minSuf(i, j - 1), ss - 2);
                    } else if (s[s.size() - ss] == '0') {
                        minim(minSuf(i - 1, j), ss - 2);
                        if (j != nonFreeO[s.size() - ss]) {
                            minim(minSuf(i, j - 1), ss - 1);
                        }
                    } else {
                        minim(minSuf(i, j - 1), ss - 2);
                        if (i != nonFreeZ[s.size() - ss]) {
                            minim(minSuf(i - 1, j), ss - 1);
                        }
                    }
                } else {
                    if (i > 0) {
                        minSuf(i - 1, j) = 0;
                    }
                    if (j > 0) {
                        minSuf(i, j - 1) = 0;
                    }
                }
            }
        }
        reverse(all(s));
        arr3d<modint> qty(s.size() + 1, zeroes + 1, ones + 1, 0);
        arr3d<modint> base(s.size() + 1, zeroes + 1, ones + 1, 0);
        base(0, 0, 0) = 1;
        qty(0, 0, 0) = 1;
        for (int i : range(s.size())) {
            for (int j : range(zeroes + 1)) {
                for (int k : range(ones + 1)) {
                    base(i + 1, j, k) += qty(i, j, k);
                    qty(i + 1, j, k) += qty(i, j, k);
                    if (s[i] == '0') {
                        if (k != ones) {
                            qty(i, j, k + 1) += qty(i, j, k);
                        }
                    } else {
                        if (j != zeroes) {
                            qty(i, j + 1, k) += qty(i, j, k);
                        }
                    }
                }
            }
        }
        Combinations c(zeroes + ones + 1);
        modint answer = 0;
        for (int i : range(zeroes + 1)) {
            for (int j : range(ones + 1)) {
                if (minSuf(i, j) > s.size()) {
                    continue;
                }
                int freeZeroes = i - nonFreeZ[s.size() - minSuf(i, j)];
                int freeOnes = j - nonFreeO[s.size() - minSuf(i, j)];
                for (int k : range(freeZeroes + 1)) {
                    for (int l : range(freeOnes + 1)) {
                        answer += base(minSuf(i, j), k, l) * c(freeZeroes - k + freeOnes - l, freeZeroes - k);
                    }
                }
            }
        }
        out.printLine(answer - 1);
    }
};


int main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(0);
#ifdef LOCAL_RELEASE
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
    auto time = clock();
#endif
    DSecretPassage solver;


    solver.solve();
    fflush(stdout);
#ifdef LOCAL_RELEASE
    cerr << double(clock() - time) / CLOCKS_PER_SEC << endl;
#endif
    return 0;
}


Measured memory_bytes: 57376