#pragma region Macros

#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,fma,abm,mmx,avx,avx2")

#include <bits/extc++.h>
// #include <atcoder/all>
// using namespace atcoder;
using namespace std;
using namespace __gnu_pbds;

// #include <boost/multiprecision/cpp_dec_float.hpp>
// #include <boost/multiprecision/cpp_int.hpp>
// namespace mp = boost::multiprecision;
// using Bint = mp::cpp_int;
// using Bdouble = mp::number<mp::cpp_dec_float<256>>;

#define pb emplace_back
#define int ll
#define endl '\n'

#define sqrt __builtin_sqrtl
#define cbrt __builtin_cbrtl
#define hypot __builtin_hypotl

// #define y0 y3487465
// #define y1 y8687969
// #define j0 j1347829
// #define j1 j234892
#define next asdnext
#define prev asdprev

using ll = long long;
using ld = long double;
const ld PI = acosl(-1);
const int INF = 1 << 30;
const ll INFL = 1LL << 61;
// const int MOD = 998244353;
const int MOD = 1000000007;

const ld EPS = 1e-10;
const bool equals(ld a, ld b) { return fabs((a) - (b)) < EPS; }

const vector<int> dx = {0, 1, 0, -1, 1, 1, -1, -1}; // → ↓ ← ↑ ↘ ↙ ↖ ↗
const vector<int> dy = {1, 0, -1, 0, 1, -1, -1, 1};

struct Edge {
    int from, to, cost;
    Edge() : from(-1), to(-1), cost(-1) {}
    Edge(int to, ll cost) : to(to), cost(cost) {}
    Edge(int from, int to, ll cost) : from(from), to(to), cost(cost) {}
};

chrono::system_clock::time_point  start, now;
__attribute__((constructor))
void constructor() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(10);
    start = chrono::system_clock::now();
}

__int128_t POW(__int128_t x, int n) {
    __int128_t ret = 1;
    assert(n >= 0);
    if (x == 1 or n == 0) ret = 1;
    else if (x == -1 && n % 2 == 0) ret = 1; 
    else if (x == -1) ret = -1; 
    else if (n % 2 == 0) {
        assert(x < INFL);
        ret = POW(x * x, n / 2);
    } else {
        assert(x < INFL);
        ret = x * POW(x, n - 1);
    }
    return ret;
}
int per(int x, int y) { // x = qy + r (0 <= r < y) を満たすq
    assert(y != 0);
    if (x >= 0 && y > 0) return x / y;
    if (x >= 0 && y < 0) return x / y - (x % y < 0);
    if (x < 0 && y < 0) return x / y + (x % y < 0);
    return x / y - (x % y < 0); //  (x < 0 && y > 0) 
}
int mod(int x, int y) { // x = qy + r (0 <= r < y) を満たすr
    assert(y != 0);
    if (x >= 0) return x % y;
    __int128_t ret = x % y; // (x < 0)
    ret += (__int128_t)abs(y) * INFL;
    ret %= abs(y);
    return ret;
}
int floor(int x, int y) { // (ld)x / y 以下の最大の整数
    assert(y != 0);
    if (y < 0) x = -x, y = -y;
    return x >= 0 ? x / y : (x + 1) / y - 1;
}
int ceil(int x, int y) { // (ld)x / y 以上の最小の整数
    assert(y != 0);
    if (y < 0) x = -x, y = -y;
    return x > 0 ? (x - 1) / y + 1 : x / y;
}
int round(int x, int y) {
    assert(y != 0);
    return (x * 2 + y) / (y * 2);
}
int round(int x, int y, int k) { // (ld)(x/y)を10^kの位に関して四捨五入
    assert(y != 0); // TODO
    return INFL;
}
int round2(int x, int y) { // 五捨五超入 // 未verify
    assert(y != 0);
    if (y < 0) y = -y, x = -x;
    int z = z / y;
    if ((z * 2 + 1) * y <= y * 2) z++;
    return z;
}
int floor(ld x, ld y) { // 誤差対策TODO
    assert(!equals(y, 0));
    return floor(x / y);
}
int ceil(ld x, ld y) { // 誤差対策TODO // ceil(p/q) = -floor(-(p/q))らしい
    assert(!equals(y, 0));
    return ceil(x / y);
}
int perl(ld x, ld y) { // x = qy + r (0 <= r < y, qは整数) を満たす q
    // 未verify. 誤差対策TODO. EPS外してもいいかも。
    assert(!equals(y, 0));
    if (x >= 0 && y > 0) return floor(x / y)+EPS;
    if (x >= 0 && y < 0) return -floor(x / fabs(y));
    if (x < 0 && y < 0) return floor(x / y) + (x - floor(x/y)*y < -EPS);
    return floor(x / y) - (x - floor(x/y)*y < -EPS); //  (x < 0 && y > 0) 
}
ld modl(ld x, ld y) { // x = qy + r (0 <= r < y, qは整数) を満たす r
    // 未verify. 誤差対策TODO. -0.0が返りうる。
    assert(!equals(y, 0));
    if (x >= 0) return x - fabs(y)*fabs(per(x, y));
    return x - fabs(y)*floor(x, fabs(y));
}
int seisuu(ld x) { return (int)x; } // 整数部分. 誤差対策TODO
int seisuu(int x, int y) {
    assert(y != 0);
    return x / y;
}
int seisuu(ld x, ld y) { // 誤差対策TODO
    assert(!equals(y, 0));
    return (int)(x / y);
}

pair<int, int> max(const pair<int, int> &a, const pair<int, int> &b) {
    if (a.first > b.first or a.first == b.first && a.second > b.second) return a;
    return b;
}
pair<int, int> min(const pair<int, int> &a, const pair<int, int> &b) {
    if (a.first < b.first or a.first == b.first && a.second < b.second) return a;
    return b;
}

template <class T> bool chmax(T &a, const T& b) {
    if (a < b) { a = b; return true; } return false;
}
template <class T> bool chmin(T &a, const T& b) {
    if (a > b) { a = b; return true; } return false;
}
template <class T> T mid(T a, T b, T c) {
    return a + b + c - max({a, b, c}) - min({a, b, c});
}
template <class T> void Sort(T &a, T &b, bool rev = false) {
    if (rev == false) { 
        if (a > b) swap(a, b);
    } else {
        if (b > a) swap(b, a);
    }
}
template <class T> void sort(T &a, T &b, T &c, bool rev = false) {
    if (rev == false) { 
        if (a > b) swap(a, b); if (a > c) swap(a, c); if (b > c) swap(b, c);
    } else {
        if (c > b) swap(c, b); if (c > a) swap(c, a); if (b > a) swap(b, a);
    }
}
template <class T> void sort(T &a, T &b, T &c, T &d, bool rev = false) {
    if (rev == false) { 
        if (a > b) swap(a, b); if (a > c) swap(a, c);  if (a > d) swap(a, d);
        if (b > c) swap(b, c); if (b > d) swap(b, d); if (c > d) swap(c, d);
    } else {
        if (d > c) swap(d, c); if (d > b) swap(d, b); if (d > a) swap(d, a);
        if (c > b) swap(c, b); if (c > a) swap(c, a); if (b > a) swap(b, a);
    }
}

int countl_zero(int x) { return __builtin_clzll(x); }
int countl_one(int x) {
    int ret = 0; while (x % 2) { x /= 2; ret++; } return ret;
}
int countr_zero(int x) { return __builtin_ctzll(x); }
int countr_one(int x) {
    int ret = 0, k = 63 - __builtin_clzll(x);
    while (k != -1 && (x & (1LL << k))) { k--; ret++; }
    return ret;
}
int popcount(int x) { return __builtin_popcountll(x); }
int unpopcount(int x) { return 64 - __builtin_clzll(x) - __builtin_popcountll(x); }

int top_bit(int x) { return 63 - __builtin_clzll(x);} // 2^kの位
int bot_bit(int x) { return __builtin_ctz(x);} // 2^kの位
int MSB(int x) { return 1 << (63 - __builtin_clzll(x)); } // mask
int LSB(int x) { return (x & -x); } // mask

int bit_width(int x) { return 64 - __builtin_clzll(x); } // 桁数
int ceil_log2(int x) { return 63 - __builtin_clzll(x); }
int bit_floor(int x) { return 1 << (63 - __builtin_clzll(x)); }
int floor_log2(int x) { return 64 - __builtin_clzll(x-1); }
int bit_ceil(int x) { return 1 << (64 - __builtin_clzll(x-1)) - (x==1); }

int hamming(int a, int b) { return popcount(a ^ b); }
int compcnt(int x) { return (popcount(x^(x >> 1)) + (x&1)) / 2; }

class UnionFind {
public:
	UnionFind() = default;
    UnionFind(int N) : par(N), sz(N, 1) {
        iota(par.begin(), par.end(), 0);
    }
	int root(int x) {
		if (par[x] == x) return x;
		return (par[x] = root(par[x]));
	}
	bool unite(int x, int y) {
		int rx = root(x);
		int ry = root(y);
        if (rx == ry) return false;
		if (sz[rx] < sz[ry]) swap(rx, ry);
		sz[rx] += sz[ry];
		par[ry] = rx;
        return true;
	}
	bool issame(int x, int y) { return (root(x) == root(y)); }
	int size(int x) { return sz[root(x)]; }
    vector<vector<int>> groups(int N) {
        vector<vector<int>> G(N);
        for (int x = 0; x < N; x++) {
            G[root(x)].push_back(x);
        }
		G.erase( remove_if(G.begin(), G.end(),
            [&](const vector<int>& V) { return V.empty(); }), G.end());
        return G;
    }
private:
	vector<int> par, sz;
};

template<typename T>
struct BIT {
    int N;               // 要素数
    vector<T> bit[2];  // データの格納先
    BIT(int N_) { init(N_); }
    void init(int N_) {
        N = N_ + 1;
        bit[0].assign(N, 0); bit[1].assign(N, 0);
    }
    void add_sub(int p, int i, T x) {
        while (i < N) { bit[p][i] += x; i += (i & -i); }
    }
    void add(int l, int r, T x) {
        add_sub(0, l + 1, -x * l); add_sub(0, r + 1, x * r);
        add_sub(1, l + 1, x); add_sub(1, r + 1, -x);
    }
    void add(int i, T x) { add(i, i + 1, x); }
    T sum_sub(int p, int i) {
        T ret = 0;
        while (i > 0) { ret += bit[p][i]; i -= (i & -i); }
        return ret;
    }
    T sum(int i) { return sum_sub(0, i) + sum_sub(1, i) * i; }
    T sum(int l, int r) { return sum(r) - sum(l); }
    T get(int i) { return sum(i, i + 1); }
    void set(int i, T x) { T s = get(i); add(i, -s + x); }
};

template<int mod> class Modint {
public:
    int val = 0;
    Modint(int x = 0) { while (x < 0) x += mod; val = x % mod; }
    Modint(const Modint &r) { val = r.val; }

    Modint operator -() { return Modint(-val); } // 単項
    Modint operator +(const Modint &r) { return Modint(*this) += r; }
    Modint operator +(const int &q) { Modint r(q); return Modint(*this) += r; }
    Modint operator -(const Modint &r) { return Modint(*this) -= r; }
    Modint operator -(const int &q) { Modint r(q); return Modint(*this) -= r; }
    Modint operator *(const Modint &r) { return Modint(*this) *= r; }
    Modint operator *(const int &q) { Modint r(q); return Modint(*this) *= r; }
    Modint operator /(const Modint &r) { return Modint(*this) /= r; }
    Modint operator /(const int &q) { Modint r(q); return Modint(*this) /= r; }
    
    Modint& operator ++() { val++; if (val >= mod) val -= mod; return *this; } // 前置
    Modint operator ++(signed) { ++*this; return *this; } // 後置
    Modint& operator --() { val--; if (val < 0) val += mod; return *this; }
    Modint operator --(signed) { --*this; return *this; }
    Modint &operator +=(const Modint &r) { val += r.val; if (val >= mod) val -= mod; return *this; }
    Modint &operator +=(const int &q) { Modint r(q); val += r.val; if (val >= mod) val -= mod; return *this; }
    Modint &operator -=(const Modint &r) { if (val < r.val) val += mod; val -= r.val; return *this; }
    Modint &operator -=(const int &q) { Modint r(q);  if (val < r.val) val += mod; val -= r.val; return *this; }
    Modint &operator *=(const Modint &r) { val = val * r.val % mod; return *this; }
    Modint &operator *=(const int &q) { Modint r(q); val = val * r.val % mod; return *this; }
    Modint &operator /=(const Modint &r) {
        int a = r.val, b = mod, u = 1, v = 0;
        while (b) {int t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v);}
        val = val * u % mod; if (val < 0) val += mod;
        return *this;
    }
    Modint &operator /=(const int &q) {
        Modint r(q); int a = r.val, b = mod, u = 1, v = 0;
        while (b) {int t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v);}
        val = val * u % mod; if (val < 0) val += mod;
        return *this;
    }
    bool operator ==(const Modint& r) { return this -> val == r.val; }
    bool operator <(const Modint& r) { return this -> val < r.val; }
    bool operator >(const Modint& r) { return this -> val > r.val; }
    bool operator !=(const Modint& r) { return this -> val != r.val; }
};

using mint = Modint<MOD>;
// using Mint = modint998244353;

istream &operator >>(istream &is, mint& x) {
    int t; is >> t; x = t; return (is);
}
ostream &operator <<(ostream &os, const mint& x) {
    return os << x.val;
}
mint modpow(const mint &x, int n) {
    if (n < 0) return (mint)1 / modpow(x, -n); // 未verify
    assert(n >= 0);
    if (n == 0) return 1;
    mint t = modpow(x, n / 2);
    t = t * t;
    if (n & 1) t = t * x;
    return t;
}

int modpow(__int128_t x, int n, int mod) {
    assert(n >= 0 && mod > 0); // TODO: n <= -1
    __int128_t ret = 1;
    while (n > 0) {
        if (n % 2 == 1) ret = ret * x % mod;
        x = x * x % mod;
        n /= 2;
    }
    return ret;
}
int modinv(__int128_t x, int mod) {
    assert(mod > 0 && x > 0);
    if (x == 1) return 1;
    return mod - modinv(mod % x, mod) * (mod / x) % mod;
}

istream &operator >>(istream &is, __int128_t& x) {
    string S; is >> S;
    __int128_t ret = 0;
    int f = 1;
    if (S[0] == '-') f = -1; 
    for (int i = 0; i < S.length(); i++)
        if ('0' <= S[i] && S[i] <= '9')
            ret = ret * 10 + S[i] - '0';
    x = ret * f;
    return (is);
}
ostream &operator <<(ostream &os, __int128_t x) {
    ostream::sentry s(os);
    if (s) {
        __uint128_t tmp = x < 0 ? -x : x;
        char buffer[128]; char *d = end(buffer);
        do {
            --d; *d = "0123456789"[tmp % 10]; tmp /= 10;
        } while (tmp != 0);
        if (x < 0) { --d; *d = '-'; }
        int len = end(buffer) - d;
        if (os.rdbuf()->sputn(d, len) != len) os.setstate(ios_base::badbit);
    }
    return os;
}

__int128_t stoll(string &S) {
    __int128_t ret = 0; int f = 1;
    if (S[0] == '-') f = -1; 
    for (int i = 0; i < S.length(); i++)
        if ('0' <= S[i] && S[i] <= '9') ret = ret * 10 + S[i] - '0';
    return ret * f;
}
__int128_t gcd(__int128_t a, __int128_t b) { return b ? gcd(b, a % b) : a; }
__int128_t lcm(__int128_t a, __int128_t b) {
    return a / gcd(a, b) * b;
    // lcmが__int128_tに収まる必要あり
}

string to_string(ld x, int k) { // xの小数第k位までをstring化する
    assert(k >= 0);
    stringstream ss;
    ss << setprecision(k + 2) << x;
    string s = ss.str();
    if (s.find('.') == string::npos) s += '.';
    int pos = s.find('.');
    for (int i = 0; k >= (int)s.size() - 1 - pos; i++) s += '0';
    s.pop_back();
    if (s.back() == '.') s.pop_back();
    return s;

    // stringstream ss; // 第k+1位を四捨五入して第k位まで返す
    // ss << setprecision(k + 1) << x;
    // string s = ss.str();
    // if (s.find('.') == string::npos) s += '.';
    // int pos = s.find('.');
    // for (int i = 0; k > (int)s.size() - 1 - pos; i++) s += '0';
    // if (s.back() == '.') s.pop_back();
    // return s;
}
string to_string(__int128_t x) {
    string ret = "";
    if (x < 0) { ret += "-"; x *= -1; }
    while (x) { ret += (char)('0' + x % 10); x /= 10; }
    reverse(ret.begin(), ret.end());
    return ret;
}
string to_string(char c) { string s = ""; s += c; return s; }

struct SXor128 {
    uint64_t x = 88172645463325252LL;
    unsigned Int() {
        x = x ^ (x << 7); return x = x ^ (x >> 9);
    }
    unsigned Int(unsigned mod) {
        x = x ^ (x << 7); x = x ^ (x >> 9); return x % mod;
    }
    unsigned Int(unsigned l, unsigned r) {
        x = x ^ (x << 7); x = x ^ (x >> 9); return x % (r - l + 1) + l;
    }
    double Double() {
        return double(Int()) / UINT_MAX;
    }
} rnd;

struct custom_hash {
    static uint64_t splitmix64(uint64_t x) {
        x += 0x9e3779b97f4a7c15;
        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
        return x ^ (x >> 31);
    }

    size_t operator()(uint64_t x) const {
        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
        return splitmix64(x + FIXED_RANDOM);
    }
};

template<class T> size_t HashCombine(const size_t seed,const T &v) {
    return seed^(hash<T>()(v)+0x9e3779b9+(seed<<6)+(seed>>2));
}
template<class T,class S> struct hash<pair<T,S>>{
    size_t operator()(const pair<T,S> &keyval) const noexcept {
        return HashCombine(hash<T>()(keyval.first), keyval.second);
    }
};
template<class T> struct hash<vector<T>>{
    size_t operator()(const vector<T> &keyval) const noexcept {
        size_t s=0;
        for (auto&& v: keyval) s=HashCombine(s,v);
        return s;
    }
};
template<int N> struct HashTupleCore{
    template<class Tuple> size_t operator()(const Tuple &keyval) const noexcept{
        size_t s=HashTupleCore<N-1>()(keyval);
        return HashCombine(s,get<N-1>(keyval));
    }
};
template <> struct HashTupleCore<0>{
    template<class Tuple> size_t operator()(const Tuple &keyval) const noexcept{ return 0; }
};
template<class... Args> struct hash<tuple<Args...>>{
    size_t operator()(const tuple<Args...> &keyval) const noexcept {
        return HashTupleCore<tuple_size<tuple<Args...>>::value>()(keyval);
    }
};

vector<mint> _fac, _finv, _inv;
void COMinit(int N) {
    _fac.resize(N + 1); _finv.resize(N + 1);  _inv.resize(N + 1);
    _fac[0] = _fac[1] = 1; _finv[0] = _finv[1] = 1; _inv[1] = 1;
    for (int i = 2; i <= N; i++) {
        _fac[i] = _fac[i-1] * mint(i);
        _inv[i] = -_inv[MOD % i] * mint(MOD / i);
        _finv[i] = _finv[i - 1] * _inv[i];
    }
}

mint FAC(int N) {
    if (N < 0) return 0; return _fac[N];
}
mint COM(int N, int K) {
    if (N < K) return 0; if (N < 0 or K < 0) return 0;
    return _fac[N] * _finv[K] * _finv[N - K];
}
mint PERM(int N, int K) {
    if (N < K) return 0; if (N < 0 or K < 0) return 0;
    return _fac[N] *  _finv[N - K];
}
mint NHK(int N, int K) {
    if (N == 0 && K == 0)  return 1;
    return COM(N + K - 1, K);
}

#pragma endregion

using i64 = int64_t;
constexpr i64 BASE = 1000000000;
constexpr signed BASE_DIGITS = 9;
struct BigInt {
    vector<i64> A;
    int sign;

    int size() const {
        if (A.empty()) return 0;
        int ret = (A.size() - 1) * BASE_DIGITS;
        i64 ca = A.back();
        while (ca) {
            ret++;
            ca /= 10;
        }
        return ret;
    }

    BigInt pow(const BigInt &v) {
        BigInt ret = 1, a = *this, b = v;
        while (!b.isZero()) {
            if (b % 2) {
                ret *= a;
            }
            a *= a, b /= 2;
        }
        return ret;
    }

    string to_string() {
        stringstream ss;
        ss << *this;
        return ss.str();
    }

    int digsum() {
        string s = to_string();
        int ret = 0;
        for (char c : s) ret += c - '0';
        return ret;
    }

    BigInt() : sign(1) {}
    BigInt(i64 v) {
        *this = v;
    }
    BigInt(const string &s) {
        read(s);
    }

    void operator=(const BigInt &v) {
        sign = v.sign;
        A = v.A;
    }

    void operator=(i64 v) {
        sign = 1;
        A.clear();
        if (v < 0) {
            sign = -1, v = -v;
        }
        for (; v > 0; v = v / BASE) {
            A.pb(v % BASE);
        }
    }

    BigInt operator+(const BigInt &v) const {
        if (sign == v.sign) {
            BigInt res = v;
            for (int i = 0, carry = 0; i < max(A.size(), v.A.size()) or carry; i++) {
                if (i == res.A.size()) {
                    res.A.pb(0);
                }
                res.A[i] += carry + (i < A.size() ? A[i] : 0);
                carry = res.A[i] >= BASE;
                if (carry) {
                    res.A[i] -= BASE;
                }
            }
            return res;
        }
        return *this - (-v);
    }

    BigInt operator-(const BigInt &v) const {
        if (sign == v.sign) {
            if (abs() >= v.abs()) {
                BigInt res = *this;
                for (int i = 0, carry = 0; i < v.A.size() or carry; i++) {
                    res.A[i] -= carry + (i < v.A.size() ? v.A[i] : 0);
                    carry = res.A[i] < 0;
                    if (carry) {
                        res.A[i] += BASE;
                    }
                }
                res.trim();
                return res;
            }
            return -(v - *this);
        }
        return *this + (-v);
    }

    void operator*=(i64 v) {
        if (v < 0) {
            sign = -sign, v = -v;
        }
        for (int i = 0, carry = 0; i < A.size() or carry; i++) {
            if (i == A.size()) {
                A.pb(0);
            }
            i64 cur = A[i] * v + carry;
            carry = cur / BASE;
            A[i] = cur % BASE;
        }
        trim();
    }

    BigInt operator*(i64 v) const {
        BigInt res = *this;
        res *= v;
        return res;
    }

    friend pair<BigInt, BigInt> divmod(const BigInt &a1, const BigInt &b1) {
        i64 norm = BASE / (b1.A.back() + 1);
        BigInt a = a1.abs() * norm;
        BigInt b = b1.abs() * norm;
        BigInt q, r;
        q.A.resize(a.A.size());

        for (int i = int(a.A.size()) - 1; i >= 0; i--) {
            r *= BASE;
            r += a.A[i];
            i64 s1 = r.A.size() <= b.A.size() ? 0 : r.A[b.A.size()];
            i64 s2 = r.A.size() <= b.A.size() - 1 ? 0 : r.A[b.A.size() - 1];
            i64 d = (BASE * s1 + s2) / b.A.back();
            r -= b * d;
            while (r < 0) {
                r += b, d--;
            }
            q.A[i] = d;
        }

        q.sign = a1.sign * b1.sign;
        r.sign = a1.sign;
        q.trim();
        r.trim();
        return make_pair(q, r / norm);
    }

    BigInt operator/(const BigInt &v) const {
        return divmod(*this, v).first;
    }

    BigInt operator%(const BigInt &v) const {
        return divmod(*this, v).second;
    }

    void operator/=(i64 v) {
        if (v < 0) {
            sign = -sign, v = -v;
        }
        for (int i = int(A.size()) - 1, rem = 0; i >= 0; i--) {
            i64 cur = A[i] + rem * BASE;
            A[i] = cur / v;
            rem = cur % v;
        }
        trim();
    }

    BigInt operator/(i64 v) const {
        BigInt res = *this;
        res /= v;
        return res;
    }

    i64 operator%(i64 v) const {
        if (v < 0) v = -v;
        i64 m = 0;
        for (int i = int(A.size()) - 1; i >= 0; i--) {
            m = (A[i] + m * BASE) % v;
        }
        return m * sign;
    }

    void operator+=(const BigInt &v) {
        *this = *this + v;
    }

    void operator-=(const BigInt &v) {
        *this = *this - v;
    }

    void operator*=(const BigInt &v) {
        *this = *this * v;
    }

    void operator/=(const BigInt &v) {
        *this = *this / v;
    }

    bool operator<(const BigInt &v) const {
        if (sign != v.sign) {
            return sign < v.sign;
        }
        if (A.size() != v.A.size()) {
            return A.size() * sign < v.A.size() * sign;
        }
        for (int i = int(A.size()) - 1; i >= 0; i--) {
            if (A[i] != v.A[i]) {
                return A[i] * sign < v.A[i] * sign;
            }
        }
        return false;
    }

    bool operator>(const BigInt &v) const {
        return v < *this;
    }

    bool operator<=(const BigInt &v) const {
        return !(v < *this);
    }

    bool operator>=(const BigInt &v) const {
        return !(*this < v);
    }

    bool operator==(const BigInt &v) const {
        return !(*this < v) && !(v < *this);
    }

    bool operator!=(const BigInt &v) const {
        return *this < v or v < *this;
    }

    void trim() {
        while (!A.empty() && !A.back()) {
            A.pop_back();
        }
        if (A.empty()) {
            sign = 1;
        }
    }

    bool isZero() const {
        return A.empty() or (A.size() == 1 && !A[0]);
    }

    BigInt operator-() const {
        BigInt res = *this;
        res.sign = -sign;
        return res;
    }

    BigInt abs() const {
        BigInt res = *this;
        res.sign = 1;
        return res;
    }

    i64 i64Value() const {
        i64 res = 0;
        for (int i = int(A.size()) - 1; i >= 0; i--) {
            res = res * BASE + A[i];
        }
        return res * sign;
    }

    friend BigInt gcd(const BigInt &a, const BigInt &b) {
        return b.isZero() ? a : gcd(b, a % b);
    }
    friend BigInt lcm(const BigInt &a, const BigInt &b) {
        return a / gcd(a, b) * b;
    }

    void read(const string &s) {
        sign = 1;
        A.clear();
        int pos = 0;
        while (pos < s.size() && (s[pos] == '-' or s[pos] == '+')) {
            if (s[pos] == '-') {
                sign = -sign;
            }
            pos++;
        }
        for (int i = int(s.size()) - 1; i >= pos; i -= BASE_DIGITS) {
            i64 x = 0;
            for (int j = max(pos, i - BASE_DIGITS + 1); j <= i; j++) {
                x = x * 10 + s[j] - '0';
            }
            A.pb(x);
        }
        trim();
    }

    friend istream& operator>>(istream &stream, BigInt &v) {
        string s;
        stream >> s;
        v.read(s);
        return stream;
    }

    friend ostream& operator<<(ostream &stream, const BigInt &v) {
        if (v.sign == -1) {
            stream << '-';
        }
        stream << (v.A.empty() ? 0 : v.A.back());
        for (int i = int(v.A.size()) - 2; i >= 0; i--) {
            stream << setw(BASE_DIGITS) << setfill('0') << v.A[i];
        }
        return stream;
    }

    static vector<i64> convert_base(const vector<i64> &a, int old_digits, int new_digits) {
        vector<i64> p(max(old_digits, new_digits) + 1);
        p[0] = 1;
        for (int i = 1; i < p.size(); i++) {
            p[i] = p[i - 1] * 10;
        }
        vector<i64> res;
        i64 cur = 0;
        int cur_digits = 0;
        for (int i = 0; i < a.size(); i++) {
            cur += a[i] * p[cur_digits];
            cur_digits += old_digits;
            while (cur_digits >= new_digits) {
                res.pb(cur % p[new_digits]);
                cur /= p[new_digits];
                cur_digits -= new_digits;
            }
        }
        res.pb(cur);
        while (!res.empty() && !res.back()) {
            res.pop_back();
        }
        return res;
    }

    static vector<i64> karatsuba(const vector<i64> &a, const vector<i64> &b) {
        int n = a.size();
        vector<i64> res(n * 2);
        if (n <= 32) {
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    res[i + j] += a[i] * b[j];
                }
            }
            return res;
        }

        int k = n >> 1;
        vector<i64> a1(a.begin(), a.begin() + k);
        vector<i64> a2(a.begin() + k, a.end());
        vector<i64> b1(b.begin(), b.begin() + k);
        vector<i64> b2(b.begin() + k, b.end());

        vector<i64> a1b1 = karatsuba(a1, b1);
        vector<i64> a2b2 = karatsuba(a2, b2);

        for (int i = 0; i < k; i++) {
            a2[i] += a1[i];
            b2[i] += b1[i];
        }

        vector<i64> r = karatsuba(a2, b2);
        for (int i = 0; i < a1b1.size(); i++) {
            r[i] -= a1b1[i];
        }
        for (int i = 0; i < a2b2.size(); i++) {
            r[i] -= a2b2[i];
        }

        for (int i = 0; i < r.size(); i++) {
            res[i + k] += r[i];
        }
        for (int i = 0; i < a1b1.size(); i++) {
            res[i] += a1b1[i];
        }
        for (int i = 0; i < a2b2.size(); i++) {
            res[i + n] += a2b2[i];
        }
        return res;
    }

    BigInt karatsubaMultiply(const BigInt &v) const {
        vector<i64> a = convert_base(this->A, BASE_DIGITS, 6);
        vector<i64> b = convert_base(v.A, BASE_DIGITS, 6);
        while (a.size() < b.size()) {
            a.pb(0);
        }
        while (b.size() < a.size()) {
            b.pb(0);
        }
        while (a.size() & (a.size() - 1)) {
            a.pb(0);
            b.pb(0);
        }
        vector<i64> c = karatsuba(a, b);
        BigInt res;
        res.sign = sign * v.sign;
        for (int i = 0, carry = 0; i < c.size(); i++) {
            i64 cur = c[i] + carry;
            res.A.pb(cur % 1000000);
            carry = cur / 1000000;
        }
        res.A = convert_base(res.A, 6, BASE_DIGITS);
        res.trim();
        return res;
    }

    static void fft(vector<complex<double>> &a, bool inv = false) {
        int n = int(a.size());
        if (n == 1) return;
        vector<complex<double>> even(n / 2), odd(n / 2);
        for (int i = 0; i < n / 2; i++) {
            even[i] = a[2 * i];
            odd[i] = a[2 * i + 1];
        }
        fft(even, inv);
        fft(odd, inv);
        complex<double> omega = polar(1.0, (-2 * inv + 1) * 2 * acos(-1) / n);
        complex<double> pow_omega = 1.0;
        for (int i = 0; i < n / 2; i++) {
            a[i] = even[i] + pow_omega * odd[i];
            a[i + n / 2] = even[i] - pow_omega * odd[i];
            pow_omega *= omega;
        }
    }

    static void conv(vector<complex<double>> &a, vector<complex<double>> &b) {
        fft(a);
        fft(b);
        int n = int(a.size());
        for (int i = 0; i < n; i++) {
            a[i] *= b[i] / complex<double>(n);
        }
        fft(a, true);
    }

    static vector<i64> conv(const vector<i64> &a, const vector<i64> &b) {
        int n = max(a.size(), b.size());
        int N = 1;
        while (N <= n) N <<= 1;
        N <<= 1;
        vector<complex<double>> ac(N), bc(N);
        for (int i = 0; i < a.size(); i++) {
            ac[i] = a[i];
        }
        for (int i = 0; i < b.size(); i++) {
            bc[i] = b[i];
        }
        conv(ac, bc);
        vector<i64> ret(ac.size());
        for (int i = 0; i < ac.size(); i++) {
            ret[i] = long(real(ac[i]) + 0.5);
        }
        return ret;
    }
    
    BigInt fftMultiply(const BigInt &v) const {
        vector<i64> a = convert_base(this->A, BASE_DIGITS, 1);
        vector<i64> b = convert_base(v.A, BASE_DIGITS, 1);
        vector<i64> c = conv(a, b);
        BigInt res;
        res.sign = sign * v.sign;
        for (int i = 0, carry = 0; i < c.size(); i++) {
            i64 cur = c[i] + carry;
            res.A.pb(cur % 10);
            carry = cur / 10;
        }
        res.A = convert_base(res.A, 1, BASE_DIGITS);
        res.trim();
        return res;
    }
    
    BigInt operator*(const BigInt &v) const {
        if (max(size(), v.size()) < 300000) {
            return karatsubaMultiply(v);
        } else {
            return fftMultiply(v);
        }
    }
};

signed main() {
    int T;
    cin >> T;
    for (int t = 0; t < T; t++) {
        BigInt N;
        int M;
        cin >> N >> M;
        BigInt ans = N * (N + 1);
        ans /= 2;
        ans = ans % M;
        cout << ans << endl;        
    }
}