Problem: This is the hard version of the problem. The only difference is that in this version 1 ≤ q ≤ 10^5. You can make hacks only if both versions of the problem are solved.

There is a process that takes place on arrays a and b of length n and length n-1 respectively. 

The process is an infinite sequence of operations. Each operation is as follows: 

  * First, choose a random integer i (1 ≤ i ≤ n-1). 
  * Then, simultaneously set a_i = min\left(a_i, \frac{a_i+a_{i+1}-b_i}{2}\right) and a_{i+1} = max\left(a_{i+1}, \frac{a_i+a_{i+1}+b_i}{2}\right) without any rounding (so values may become non-integer). 

See notes for an example of an operation.

It can be proven that array a converges, i. e. for each i there exists a limit a_i converges to. Let function F(a, b) return the value a_1 converges to after a process on a and b.

You are given array b, but not array a. However, you are given a third array c. Array a is good if it contains only integers and satisfies 0 ≤ a_i ≤ c_i for 1 ≤ i ≤ n.

Your task is to count the number of good arrays a where F(a, b) ≥ x for q values of x. Since the number of arrays can be very large, print it modulo 10^9+7.

Input

The first line contains a single integer n (2 ≤ n ≤ 100).

The second line contains n integers c_1, c_2 …, c_n (0 ≤ c_i ≤ 100).

The third line contains n-1 integers b_1, b_2, …, b_{n-1} (0 ≤ b_i ≤ 100).

The fourth line contains a single integer q (1 ≤ q ≤ 10^5).

The fifth line contains q space separated integers x_1, x_2, …, x_q (-10^5 ≤ x_i ≤ 10^5).

Output

Output q integers, where the i-th integer is the answer to the i-th query, i. e. the number of good arrays a where F(a, b) ≥ x_i modulo 10^9+7.

Example

Input


3
2 3 4
2 1
5
-1 0 1 -100000 100000


Output


56
28
4
60
0

Note

The following explanation assumes b = [2, 1] and c=[2, 3, 4] (as in the sample).

Examples of arrays a that are not good: 

  * a = [3, 2, 3] is not good because a_1 > c_1; 
  * a = [0, -1, 3] is not good because a_2 < 0. 



One possible good array a is [0, 2, 4]. We can show that no operation has any effect on this array, so F(a, b) = a_1 = 0.

Another possible good array a is [0, 1, 4]. In a single operation with i = 1, we set a_1 = min((0+1-2)/(2), 0) and a_2 = max((0+1+2)/(2), 1). So, after a single operation with i = 1, a becomes equal to [-1/2, 3/2, 4]. We can show that no operation has any effect on this array, so F(a, b) = -1/2.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#define fr first
#define sc second
#define m_p make_pair
#define all(x) (x).begin(), (x).end()
#define unique(a) a.resize(unique(a.begin(), a.end()) - a.begin())
#define low_bo(a, x) ((int)(lower_bound(a.begin(), a.end(), x) - a.begin()))
#define up_bo(a, x) ((int)(upper_bound(a.begin(), a.end(), x) - a.begin()))

using namespace std;

mt19937 rnd(223);

#define TIME (clock() * 1.0 / CLOCKS_PER_SEC)
using ll = long long;
using ld = double;

namespace Ment {
    template<typename T>
    T inverse(T a, T m) {
        T u = 0, v = 1;
        while (a != 0) {
            T t = m / a;
            m -= t * a;
            swap(a, m);
            u -= t * v;
            swap(u, v);
        }
        assert(m == 1);
        return u;
    }

    template<typename T>
    class Modular {
    public:
        using Type = typename decay<decltype(T::value)>::type;

        constexpr Modular() : value() {}

        template<typename U>
        Modular(const U &x) {
            value = normalize(x);
        }

        template<typename U>
        static Type normalize(const U &x) {
            Type v;
            if (-mod() <= x && x < mod()) v = static_cast<Type>(x);
            else v = static_cast<Type>(x % mod());
            if (v < 0) v += mod();
            return v;
        }

        const Type &operator()() const { return value; }

        template<typename U>
        explicit operator U() const { return static_cast<U>(value); }

        constexpr static Type mod() { return T::value; }

        Modular &operator+=(const Modular &other) {
            if ((value += other.value) >= mod()) value -= mod();
            return *this;
        }

        Modular &operator-=(const Modular &other) {
            if ((value -= other.value) < 0) value += mod();
            return *this;
        }

        template<typename U>
        Modular &operator+=(const U &other) { return *this += Modular(other); }

        template<typename U>
        Modular &operator-=(const U &other) { return *this -= Modular(other); }

        Modular &operator++() { return *this += 1; }

        Modular &operator--() { return *this -= 1; }

        Modular operator++(int) {
            Modular result(*this);
            *this += 1;
            return result;
        }

        Modular operator--(int) {
            Modular result(*this);
            *this -= 1;
            return result;
        }

        Modular operator-() const { return Modular(-value); }

        template<typename U = T>
        typename enable_if<is_same<typename Modular<U>::Type, int>::value, Modular>::type &
        operator*=(const Modular &rhs) {
#ifdef _WIN32
            uint64_t x = static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value);
            uint32_t xh = static_cast<uint32_t>(x >> 32), xl = static_cast<uint32_t>(x), d, m;
            asm(
            "divl %4; \n\t"
            : "=a" (d), "=d" (m)
            : "d" (xh), "a" (xl), "r" (mod())
            );
            value = m;
#else
            value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value));
#endif
            return *this;
        }

        template<typename U = T>
        typename enable_if<is_same<typename Modular<U>::Type, int64_t>::value, Modular>::type &
        operator*=(const Modular &rhs) {
            int64_t q = static_cast<int64_t>(static_cast<long double>(value) * rhs.value / mod());
            value = normalize(value * rhs.value - q * mod());
            return *this;
        }

        template<typename U = T>
        typename enable_if<!is_integral<typename Modular<U>::Type>::value, Modular>::type &
        operator*=(const Modular &rhs) {
            value = normalize(value * rhs.value);
            return *this;
        }

        Modular &operator/=(const Modular &other) { return *this *= Modular(inverse(other.value, mod())); }

        template<typename U>
        friend bool operator==(const Modular<U> &lhs, const Modular<U> &rhs);

        template<typename U>
        friend bool operator<(const Modular<U> &lhs, const Modular<U> &rhs);

        template<typename U>
        friend std::istream &operator>>(std::istream &stream, Modular<U> &number);

    private:
        Type value;
    };

    template<typename T>
    bool operator==(const Modular<T> &lhs, const Modular<T> &rhs) { return lhs.value == rhs.value; }

    template<typename T, typename U>
    bool operator==(const Modular<T> &lhs, U rhs) { return lhs == Modular<T>(rhs); }

    template<typename T, typename U>
    bool operator==(U lhs, const Modular<T> &rhs) { return Modular<T>(lhs) == rhs; }

    template<typename T>
    bool operator!=(const Modular<T> &lhs, const Modular<T> &rhs) { return !(lhs == rhs); }

    template<typename T, typename U>
    bool operator!=(const Modular<T> &lhs, U rhs) { return !(lhs == rhs); }

    template<typename T, typename U>
    bool operator!=(U lhs, const Modular<T> &rhs) { return !(lhs == rhs); }

    template<typename T>
    bool operator<(const Modular<T> &lhs, const Modular<T> &rhs) { return lhs.value < rhs.value; }

    template<typename T>
    Modular<T> operator+(const Modular<T> &lhs, const Modular<T> &rhs) { return Modular<T>(lhs) += rhs; }

    template<typename T, typename U>
    Modular<T> operator+(const Modular<T> &lhs, U rhs) { return Modular<T>(lhs) += rhs; }

    template<typename T, typename U>
    Modular<T> operator+(U lhs, const Modular<T> &rhs) { return Modular<T>(lhs) += rhs; }

    template<typename T>
    Modular<T> operator-(const Modular<T> &lhs, const Modular<T> &rhs) { return Modular<T>(lhs) -= rhs; }

    template<typename T, typename U>
    Modular<T> operator-(const Modular<T> &lhs, U rhs) { return Modular<T>(lhs) -= rhs; }

    template<typename T, typename U>
    Modular<T> operator-(U lhs, const Modular<T> &rhs) { return Modular<T>(lhs) -= rhs; }

    template<typename T>
    Modular<T> operator*(const Modular<T> &lhs, const Modular<T> &rhs) { return Modular<T>(lhs) *= rhs; }

    template<typename T, typename U>
    Modular<T> operator*(const Modular<T> &lhs, U rhs) { return Modular<T>(lhs) *= rhs; }

    template<typename T, typename U>
    Modular<T> operator*(U lhs, const Modular<T> &rhs) { return Modular<T>(lhs) *= rhs; }

    template<typename T>
    Modular<T> operator/(const Modular<T> &lhs, const Modular<T> &rhs) { return Modular<T>(lhs) /= rhs; }

    template<typename T, typename U>
    Modular<T> operator/(const Modular<T> &lhs, U rhs) { return Modular<T>(lhs) /= rhs; }

    template<typename T, typename U>
    Modular<T> operator/(U lhs, const Modular<T> &rhs) { return Modular<T>(lhs) /= rhs; }

    template<typename T, typename U>
    Modular<T> power(const Modular<T> &a, const U &b) {
        assert(b >= 0);
        Modular<T> x = a, res = 1;
        U p = b;
        while (p > 0) {
            if (p & 1) res *= x;
            x *= x;
            p >>= 1;
        }
        return res;
    }

    template<typename T>
    string to_string(const Modular<T> &number) {
        return to_string(number());
    }

    template<typename T>
    std::ostream &operator<<(std::ostream &stream, const Modular<T> &number) {
        return stream << number();
    }

    template<typename T>
    std::istream &operator>>(std::istream &stream, Modular<T> &number) {
        typename common_type<typename Modular<T>::Type, int64_t>::type x;
        stream >> x;
        number.value = Modular<T>::normalize(x);
        return stream;
    }

    constexpr int md = 1e9+7;
    using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;
}
using Ment::Mint;

const int maxn = 1e4 + 110, inf = 1e9 + 100;

int n, c[200], b[200];

Mint dp[2][maxn];

const int maxw = 2e5 + 100, BG = 1e5;

Mint ans[maxw];

int B[200];

Mint ez;

void prec() {
    ez = 1;
    int BB = 0, sb = 0;
    for (int i = 0; i < n; i++) {
        ez *= c[i] + 1;
        B[i] = BB;
        if (i + 1 < n) {
            sb += b[i];
            BB += sb;
        }
    }
}

void go(int x) {
    if (x * n + B[n - 1] > 100 * n) {
        return;
    }
    if (x * n + B[n - 1] <= 0) {
        ans[x + BG] = ez;
        return;
    }
    int BIG = 1e4;
    for (int i = 0; i <= BIG; i++)
        dp[0][i] = dp[1][i] = 0;
    dp[0][0] = 1;
    dp[0][1] = -1;
    int Cs = 0;
    for (int i = 0; i < n; i++) {
        int t = (i & 1);
        for (int j = 0; j <= Cs + c[i]; j++)
            dp[!t][j] = 0;
        Mint s = 0;
        for (int A = 0; A <= Cs; A++) {
                s += dp[t][A];
                if (s != 0) {
                    // 0 <= j <= c[i]
                    // A + j - B >= x * (i + 1)
                    // j >= x * (i + 1) + B - A
                    int l = max(0, x * (i + 1) + B[i] - A);
                    int r = c[i];
                    if (l <= r) {
                        dp[!t][A + l] += s;
                        dp[!t][A + r + 1] -= s;
                    }
                }
            }
        Cs += c[i];
    }
    Mint s = 0;
    int t = (n & 1);
    for (int i = 0; i <= Cs; i++) {
        s += dp[t][i];
        ans[x + BG] += s;
    }
}

void solve() {
    n = 100;
    cin >> n;
    for (int i = 0; i < n; i++) {
        c[i] = 100;
        cin >> c[i];
    }
    for (int i = 0; i < n - 1; i++) {
        b[i] = 10;
        cin >> b[i];
    }
    prec();
    for (int x = -BG; x <= BG; x++)
        go(x);
    int zap;
    cin >> zap;
    while (zap--) {
        int x;
        cin >> x;
        cout << ans[x + BG] << '\n';
    }
}

int main() {
#ifdef ONPC
    freopen("../a.in", "r", stdin);
    //freopen("../a.out", "w", stdout);
#endif
    ios::sync_with_stdio(0);
    cin.tie(0);
    cout << fixed;
    cout.precision(20);
    solve();
    cerr << "\n\nConsumed " << TIME;
}