#220356 (D) No.579 3 x N グリッド上のサイクルのサイズ(hard)

提出ソース
結果

問題	No.579 3 x N グリッド上のサイクルのサイズ(hard)
ユーザー	yosupot
提出日時	2017-12-02 21:18:40
言語	D (dmd 2.106.1)
結果	AC
実行時間	10 ms / 2,000 ms
コード長	29,701 bytes
コンパイル時間	2,212 ms
コンパイル使用メモリ	168,052 KB
実行使用メモリ	5,376 KB
最終ジャッジ日時	2024-06-12 22:46:30
合計ジャッジ時間	4,739 ms
ジャッジサーバーID （参考情報）	judge2 / judge3
このコードへのチャレンジ
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テストケース

テストケース表示
入力	結果	実行時間実行使用メモリ
testcase_00	AC	1 ms 5,248 KB
testcase_01	AC	1 ms 5,376 KB
testcase_02	AC	2 ms 5,376 KB
testcase_03	AC	1 ms 5,376 KB
testcase_04	AC	1 ms 5,376 KB
testcase_05	AC	2 ms 5,376 KB
testcase_06	AC	1 ms 5,376 KB
testcase_07	AC	1 ms 5,376 KB
testcase_08	AC	2 ms 5,376 KB
testcase_09	AC	2 ms 5,376 KB
testcase_10	AC	2 ms 5,376 KB
testcase_11	AC	1 ms 5,376 KB
testcase_12	AC	2 ms 5,376 KB
testcase_13	AC	2 ms 5,376 KB
testcase_14	AC	2 ms 5,376 KB
testcase_15	AC	2 ms 5,376 KB
testcase_16	AC	2 ms 5,376 KB
testcase_17	AC	2 ms 5,376 KB
testcase_18	AC	2 ms 5,376 KB
testcase_19	AC	2 ms 5,376 KB
testcase_20	AC	3 ms 5,376 KB
testcase_21	AC	3 ms 5,376 KB
testcase_22	AC	4 ms 5,376 KB
testcase_23	AC	4 ms 5,376 KB
testcase_24	AC	3 ms 5,376 KB
testcase_25	AC	3 ms 5,376 KB
testcase_26	AC	3 ms 5,376 KB
testcase_27	AC	3 ms 5,376 KB
testcase_28	AC	3 ms 5,376 KB
testcase_29	AC	4 ms 5,376 KB
testcase_30	AC	4 ms 5,376 KB
testcase_31	AC	4 ms 5,376 KB
testcase_32	AC	3 ms 5,376 KB
testcase_33	AC	4 ms 5,376 KB
testcase_34	AC	4 ms 5,376 KB
testcase_35	AC	3 ms 5,376 KB
testcase_36	AC	3 ms 5,376 KB
testcase_37	AC	3 ms 5,376 KB
testcase_38	AC	4 ms 5,376 KB
testcase_39	AC	4 ms 5,376 KB
testcase_40	AC	6 ms 5,376 KB
testcase_41	AC	5 ms 5,376 KB
testcase_42	AC	5 ms 5,376 KB
testcase_43	AC	5 ms 5,376 KB
testcase_44	AC	6 ms 5,376 KB
testcase_45	AC	5 ms 5,376 KB
testcase_46	AC	6 ms 5,376 KB
testcase_47	AC	5 ms 5,376 KB
testcase_48	AC	5 ms 5,376 KB
testcase_49	AC	6 ms 5,376 KB
testcase_50	AC	6 ms 5,376 KB
testcase_51	AC	5 ms 5,376 KB
testcase_52	AC	6 ms 5,376 KB
testcase_53	AC	5 ms 5,376 KB
testcase_54	AC	6 ms 5,376 KB
testcase_55	AC	6 ms 5,376 KB
testcase_56	AC	5 ms 5,376 KB
testcase_57	AC	6 ms 5,376 KB
testcase_58	AC	5 ms 5,376 KB
testcase_59	AC	6 ms 5,376 KB
testcase_60	AC	9 ms 5,376 KB
testcase_61	AC	10 ms 5,376 KB
testcase_62	AC	9 ms 5,376 KB
testcase_63	AC	10 ms 5,376 KB
testcase_64	AC	9 ms 5,376 KB
testcase_65	AC	10 ms 5,376 KB
testcase_66	AC	10 ms 5,376 KB
testcase_67	AC	9 ms 5,376 KB
testcase_68	AC	9 ms 5,376 KB
testcase_69	AC	10 ms 5,376 KB
testcase_70	AC	10 ms 5,376 KB
testcase_71	AC	10 ms 5,376 KB
testcase_72	AC	10 ms 5,376 KB
testcase_73	AC	9 ms 5,376 KB
testcase_74	AC	9 ms 5,376 KB
testcase_75	AC	10 ms 5,376 KB
testcase_76	AC	10 ms 5,376 KB
testcase_77	AC	10 ms 5,376 KB
testcase_78	AC	10 ms 5,376 KB
testcase_79	AC	9 ms 5,376 KB
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ソースコード

raw source code
/+ dub.sdl:
    name "A"
    dependency "dcomp" version=">=0.7.4"
+/
 
import std.stdio, std.algorithm, std.range, std.conv;
// import dcomp.foundation, dcomp.scanner;
// import dcomp.numeric.convolution;
// import dcomp.modint;
// import dcomp.modpoly;
immutable int MD = 10^^9 + 7;

alias Mint = ModInt!MD;
alias MPol = ModPoly!MD;


int main() {
    auto po = [
        0,
        32,
        316,
        2292,
        14422,
        84744,
        479004,
        2638328,
        14258574,
        75940592,
        399782668,
        84795558,
        786749020,
        442043859,
        352536615,
        76576421,
        744912747,
        420315017,
        25759333,
        562730793,
        424899366,
        153177921,
        250747498,
        306910436,
        324829483,
        572545341,
        104022619,
        226237183,
        421453002,
        754280938,
        291624319,
        60437277,
        297658752,
        677142927,
        63550828,
        801541292,
        683008492,
        650348,
        519624175,
        715484025,
        724658778,
        152363657,
        280344328,
        892278238,
        206785631,
        227202296,
        788486407,
        392284243,
        927772200,
        781378846,
        881515964,
        905982211,
        674841192,
        139044658,
        711210295,
        384364637,
        137653614,
        441363040,
        812818651,
        929556368,
        494420762,
        802527485,
        700803632,
        461521718,
        152786116,
        688977792,
        48724029,
        642700933,
        15567410,
        246397043,
        859581827,
        685250826,
        120226158,
        551687712,
        987163282,
        422276494,
        570671107,
        813070470,
        429968009,
        849487586,
        453150672,
        606112895,
        921636591,
        961537190,
        68995663,
        873642098,
        377371441,
        101407285,
        187434129,
        180415383,
        920712750,
        544594592,
        402649575,
        549811430,
        619506771,
        426917748,
        274013175,
        615469131,
        800944525,
        925880089,
    ].map!(x => Mint(x)).array;

    auto pol = MPol(po);

    auto v = berlekampMassey(po);

//    writeln(v);

    long x;
    sc.read(x);
    auto z = nthMod(x, v);
    Mint sm = 0;
    foreach (i, d; po) {
        sm += d * z[i];
    }
    writeln(sm);
//    for (int i: rng(int(v.size()))) {
//        sm += po[i] * z.freq(i);
//    }
//    cout << to_string(z) << endl;
//    cout << sm.v << endl;*/
    return 0;
}

Scanner sc;
static this() {
    sc = new Scanner(stdin);
}
/* IMPORT /home/yosupo/Program/dcomp/source/dcomp/modpoly.d */
// module dcomp.modpoly;

// import dcomp.numeric.primitive;
// import dcomp.numeric.convolution;
// import dcomp.modint;
// import dcomp.container.stack;


struct ModPoly(uint MD) if (MD < int.max) {
    alias Mint = ModInt!MD;
    import std.algorithm : min, max, reverse;
    
    Stack!Mint d;
    void shrink() { while (!d.empty && d.back == Mint(0)) d.removeBack; }
    @property size_t length() const { return d.length; }
    @property inout(Mint)[] data() inout { return d.data; }
    
    this(in Mint[] v) {
        d = v.dup;
        shrink();
    }

    const(Mint) opIndex(size_t i) const {
        if (i < d.length) return d[i];
        return Mint(0);
    }
    void opIndexAssign(Mint x, size_t i) {
        if (i < d.length) {
            d[i] = x;
            shrink();
            return;
        }
        if (x == Mint(0)) return;
        while (d.length < i) d.insertBack(Mint(0));
        d.insertBack(x);
        return;
    }

    ModPoly opBinary(string op : "+")(in ModPoly r) const {
        size_t N = length, M = r.length;
        Mint[] res = new Mint[max(N, M)];
        foreach (i; 0..max(N, M)) res[i] = this[i] + r[i];
        return ModPoly(res);
    }
    ModPoly opBinary(string op : "-")(in ModPoly r) const {
        size_t N = length, M = r.length;
        Mint[] res = new Mint[max(N, M)];
        foreach (i; 0..max(N, M)) res[i] = this[i] - r[i];
        return ModPoly(res);
    }
    ModPoly opBinary(string op : "*")(in ModPoly r) const {
        size_t N = length, M = r.length;
        if (min(N, M) == 0) return ModPoly();
        return ModPoly(multiply(data, r.data));
    }
    ModPoly opBinary(string op : "*")(in Mint r) const {
        Mint[] res = new Mint[length];
        foreach (i; 0..length) res[i] = this[i]*r;
        return ModPoly(res);
    }
    ModPoly opBinary(string op : "/")(in ModPoly r) const {
        size_t B = max(1, length, r.length);
        return divWithInv(r.inv(B), B);
    }
    ModPoly opBinary(string op : "%")(in ModPoly r) const {
        return *this - y * div(y);
    }
    ModPoly opBinary(string op : "<<")(size_t n) const {
        Mint[] res = new Mint[n+length];
        foreach (i; 0..length) res[i+n] = this[i];
        return ModPoly(res);
    }
    ModPoly opBinary(string op : ">>")(size_t n) const {
        if (length <= n) return ModPoly();
        Mint[] res = new Mint[length-n];
        foreach (i; n..length) res[i-n] = this[i];
        return ModPoly(res);
    }
    ModPoly opOpAssign(string op)(in ModPoly r) {
        return mixin("this=this"~op~"r");
    }

    ModPoly strip(size_t n) const {
        auto res = d.data.dup;
        res = res[0..min(n, length)];
        return ModPoly(res);
    }
    ModPoly divWithInv(in ModPoly ir, size_t B) const {
        return (this * ir) >> (B-1);
    }
    ModPoly remWithInv(in ModPoly r, in ModPoly ir, size_t B) const {
        return this - r * divWithInv(ir, B);
    }
    ModPoly rev(ptrdiff_t n = -1) const {
        auto res = d.data.dup;
        if (n != -1) res = res[0..n];
        reverse(res);
        return ModPoly(res);
    }
    ModPoly inv(size_t n) const {
        assert(length >= 1);
        assert(n >= length-1);
        ModPoly c = rev();
        ModPoly d = ModPoly([Mint(1)/c[0]]);
        for (ptrdiff_t i = 1; i+length-2 < n; i *= 2) {
            d = (d * (ModPoly([Mint(2)]) - c*d)).strip(2*i);
        }
        return d.rev(n+1-length);
    }

    string toString() {
        import std.conv : to;
        import std.range : join;
        string[] l = new string[length];
        foreach (i; 0..length) {
            l[i] = (this[i]).toString ~ "x^" ~ i.to!string;
        }
        return l.join(" + ");
    }
}

ModPoly!MD nthMod(uint MD)(ulong n, in ModPoly!MD mod) {
    import core.bitop : bsr;
    alias Mint = ModInt!MD;
    assert(mod.length);
    size_t B = mod.length * 2 - 1;
    auto modInv = mod.inv(B);
    auto p = ModPoly!MD([Mint(1)]);
    if (n == 0) return p;
    auto m = bsr(n);
    foreach_reverse(i; 0..m+1) {
        if (n & (1L<<i)) {
            p = (p<<1).remWithInv(mod, modInv, B);
        }
        if (i) {
            p = (p*p).remWithInv(mod, modInv, B);
        }
    }
    return p;
}

ModPoly!MD berlekampMassey(uint MD)(in ModInt!MD[] s) {
    alias Mint = ModInt!MD;
    Mint[] b = [Mint(-1)], c = [Mint(-1)];
    Mint y = 1;
    foreach (ed; 1..s.length+1) {
        auto L = c.length, M = b.length;
        Mint x = 0;
        foreach (i; 0..L) {
            x += c[i] * s[ed-L+i];
        }
        b ~= Mint(0); M++;
        if (x == Mint(0)) {
            continue;
        }
        auto freq = x/y;
        if (L < M) {
            auto tmp = c;
            import std.range : repeat, take, array;
            c = Mint(0).repeat.take(M-L).array ~ c;
            foreach (i; 0..M) {
                c[M-1-i] -= freq*b[M-1-i];
            }
            b = tmp;
            y = x;
        } else {
            foreach (i; 0..M) {
                c[L-1-i] -= freq*b[M-1-i];
            }
        }
    }
    return ModPoly!MD(c);
}

 

 
/* IMPORT /home/yosupo/Program/dcomp/source/dcomp/modint.d */
// module dcomp.modint;

// import dcomp.numeric.primitive;

 
struct ModInt(uint MD) if (MD < int.max) {
    import std.conv : to;
    uint v;
    this(int v) {this(long(v));}
    this(long v) {this.v = (v%MD+MD)%MD;}
    static auto normS(uint x) {return (x<MD)?x:x-MD;}
    static auto make(uint x) {ModInt m; m.v = x; return m;}
     
    auto opBinary(string op:"+")(ModInt r) const {return make(normS(v+r.v));}
     
    auto opBinary(string op:"-")(ModInt r) const {return make(normS(v+MD-r.v));}
     
    auto opBinary(string op:"*")(ModInt r) const {return make((ulong(v)*r.v%MD).to!uint);}
     
    auto opBinary(string op:"/")(ModInt r) const {return this*inv(r);}
    auto opOpAssign(string op)(ModInt r) {return mixin ("this=this"~op~"r");}
     
    static ModInt inv(ModInt x) {return ModInt(extGcd!int(x.v, MD)[0]);}
    string toString() const {return v.to!string;}
}

 
 

 

 
struct DModInt(string name) {
    import std.conv : to;
    static uint MD;
    uint v;
    this(int v) {this(long(v));}
    this(long v) {this.v = ((v%MD+MD)%MD).to!uint;}
    static auto normS(uint x) {return (x<MD)?x:x-MD;}
    static auto make(uint x) {DModInt m; m.MD = MD; m.v = x; return m;}
     
    auto opBinary(string op:"+")(DModInt r) const {return make(normS(v+r.v));}
     
    auto opBinary(string op:"-")(DModInt r) const {return make(normS(v+MD-r.v));}
     
    auto opBinary(string op:"*")(DModInt r) const {return make((ulong(v)*r.v%MD).to!uint);}
     
    auto opBinary(string op:"/")(DModInt r) const {return this*inv(r);}
    auto opOpAssign(string op)(DModInt r) {return mixin ("this=this"~op~"r");}
     
    static DModInt inv(DModInt x) {
        return DModInt(extGcd!int(x.v, MD)[0]);
    }
    string toString() {return v.to!string;}
}

 
 

 

template isModInt(T) {
    const isModInt =
        is(T : ModInt!MD, uint MD) || is(S : DModInt!S, string s);
}


T[] factTable(T)(size_t length) if (isModInt!T) {
    import std.range : take, recurrence;
    import std.array : array;
    return T(1).recurrence!((a, n) => a[n-1]*T(n)).take(length).array;
}

 
T[] invFactTable(T)(size_t length) if (isModInt!T) {
    import std.algorithm : map, reduce;
    import std.range : take, recurrence, iota;
    import std.array : array;
    auto res = new T[length];
    res[$-1] = T(1) / iota(1, length).map!T.reduce!"a*b";
    foreach_reverse (i, v; res[0..$-1]) {
        res[i] = res[i+1] * T(i+1);
    }
    return res;
}

T[] invTable(T)(size_t length) if (isModInt!T) {
    auto f = factTable!T(length);
    auto invf = invFactTable!T(length);
    auto res = new T[length];
    foreach (i; 1..length) {
        res[i] = invf[i] * f[i-1];
    }
    return res;
}

 
/* IMPORT /home/yosupo/Program/dcomp/source/dcomp/numeric/convolution.d */
// module dcomp.numeric.convolution;

 
T[] zeta(T)(T[] v, bool rev) {
    import core.bitop : bsr;
    int n = bsr(v.length);
    assert(1<<n == v.length);
    foreach (fe; 0..n) {
        foreach (i, _; v) {
            if (i & (1<<fe)) continue;
            if (!rev) {
                v[i] += v[i|(1<<fe)];
            } else {
                v[i] -= v[i|(1<<fe)];
            }
        }
    }
    return v;
}

 
T[] hadamard(T)(T[] v, bool rev) {
    import core.bitop : bsr;
    int n = bsr(v.length);
    assert(1<<n == v.length);
    foreach (fe; 0..n) {
        foreach (i, _; v) {
            if (i & (1<<fe)) continue;
            auto l = v[i], r = v[i|(1<<fe)];
            if (!rev) {
                v[i] = l+r;
                v[i|(1<<fe)] = l-r;
            } else {
                v[i] = (l+r)/2;
                v[i|(1<<fe)] = (l-r)/2;
            }
        }
    }
    return v;
}

import std.complex;

double[] fftSinList(size_t S) {
    import std.math : PI, sin;
    assert(2 <= S);
    size_t N = 1<<S;
    static double[][30] buf;
    if (!buf[S].length) {
        buf[S] = new double[3*N/4+1];
        foreach (i; 0..N/4+1) {
            buf[S][i] = sin(i*2*double(PI)/N);
            buf[S][N/2-i] = buf[S][i];
            buf[S][N/2+i] = -buf[S][i];
        }
    }
    return buf[S];
}

void fft(bool type)(Complex!double[] c) {
    import std.algorithm : swap;
    import core.bitop : bsr;
    alias P = Complex!double;
    size_t N = c.length;
    assert(N);
    size_t S = bsr(N);
    assert(1<<S == N);
    if (S == 1) {
        auto x = c[0], y = c[1];
        c[0] = x+y;
        c[1] = x-y;
        return;
    }
    auto rot = fftSinList(S);
    P[] a = c.dup, b = new P[c.length];
    foreach (i; 1..S+1) {
        size_t W = 1<<(S-i);
        for (size_t y = 0; y < N/2; y += W) {
            P now = P(rot[y + N/4], rot[y]);
            if (type) now = conj(now);
            foreach (x; 0..W) {
                auto l =       a[y<<1 | x];
                auto r = now * a[y<<1 | x | W];
                b[y | x]        = l+r;
                b[y | x | N>>1] = l-r;
            }
        }
        swap(a, b);
    }
    c[] = a[];
}

double[] multiply(in double[] a, in double[] b) {
    alias P = Complex!double;
    size_t A = a.length, B = b.length;
    if (!A || !B) return [];
    size_t lg = 1;
    while ((1<<lg) < A+B-1) lg++;
    size_t N = 1<<lg;
    P[] d = new P[N];
    d[] = P(0, 0);
    foreach (i; 0..A) d[i].re = a[i];
    foreach (i; 0..B) d[i].im = b[i];
    fft!false(d);
    foreach (i; 0..N/2+1) {
        auto j = i ? (N-i) : 0;
        P x = P(d[i].re+d[j].re, d[i].im-d[j].im);
        P y = P(d[i].im+d[j].im, -d[i].re+d[j].re);
        d[i] = x * y / 4;
        if (i != j) d[j] = conj(d[i]);
    }
    fft!true(d);
    double[] c = new double[A+B-1];
    foreach (i; 0..A+B-1) {
        c[i] = d[i].re / N;
    }
    return c;
}

 

// import dcomp.modint, dcomp.numeric.primitive;

void nft(uint G, bool type, Mint)(Mint[] c) {
    import std.algorithm : swap;
    import core.bitop : bsr;    
    size_t N = c.length;
    assert(N);
    size_t S = bsr(N);
    assert(1<<S == N);

    Mint[] a = c.dup, b = new Mint[N];
    foreach (i; 1..S+1) {
        size_t W = 1<<(S-i);
        Mint base = pow(Mint(G), Mint(-1).v/(1<<i));
        if (type) base = Mint(1)/base;
        Mint now = 1;
        for (size_t y = 0; y < N/2; y += W) {
            foreach (x; 0..W) {
                auto l =       a[y<<1 | x];
                auto r = now * a[y<<1 | x | W];
                b[y | x]        = l+r;
                b[y | x | N>>1] = l-r;
            }
            now *= base;
        }
        swap(a, b);
    }
    c[] = a[];    
}

Mint[] multiply(uint G, Mint)(in Mint[] a, in Mint[] b) {
    size_t A = a.length, B = b.length;
    if (!A || !B) return [];
    size_t lg = 1;
    while ((1<<lg) < A+B-1) lg++;
    size_t N = 1<<lg;
    Mint[] _a = new Mint[N];
    Mint[] _b = new Mint[N];
    foreach (i; 0..A) _a[i] = a[i];
    foreach (i; 0..B) _b[i] = b[i];
    nft!(G, false)(_a);
    nft!(G, false)(_b);
    foreach (i; 0..N) _a[i] *= _b[i];
    nft!(G, true)(_a);
    Mint[] c = new Mint[A+B-1];
    Mint iN = Mint(1) / Mint(N);
    foreach (i; 0..A+B-1) {
        c[i] = _a[i] * iN;
    }
    return c;
}

Mint[] multiply(Mint, size_t M = 3, size_t W = 10)(in Mint[] a, in Mint[] b)
if (isModInt!Mint) {
    import std.math : round;
    alias P = Complex!double;

    size_t A = a.length, B = b.length;
    if (!A || !B) return [];
    auto N = A + B - 1;
    size_t lg = 1;
    while ((1<<lg) < N) lg++;
    N = 1<<lg;

    P[][M] x, y;
    P[] w = new P[N];
    foreach (ph; 0..M) {
        x[ph] = new P[N];
        y[ph] = new P[N];
        w[] = P(0, 0);
        foreach (i; 0..A) w[i].re = (a[i].v >> (ph*W)) % (1<<W);
        foreach (i; 0..B) w[i].im = (b[i].v >> (ph*W)) % (1<<W);
        fft!false(w);
        foreach (i; 0..N) w[i] *= 0.5;
        foreach (i; 0..N) {
            auto j = i ? N-i : 0;
            x[ph][i] = P(w[i].re+w[j].re,  w[i].im-w[j].im);
            y[ph][i] = P(w[i].im+w[j].im, -w[i].re+w[j].re);
        }
    }

    Mint[] c = new Mint[A+B-1];
    Mint basel = 1, baser = pow(Mint(1<<W), M);
    P[] z = new P[N];
    foreach (ph; 0..M) {
        z[] = P(0, 0);
        foreach (af; 0..ph+1) {
            auto bf = ph - af;
            foreach (i; 0..N) {
                z[i] += x[af][i] * y[bf][i];
            }
        }
        foreach (af; ph+1..M) {
            auto bf = ph + M - af;
            foreach (i; 0..N) {
                z[i] += x[af][i] * y[bf][i] * P(0, 1);
            }
        }
        fft!true(z);
        foreach (i; 0..A+B-1) {
            z[i] *= 1.0/N;
            c[i] += Mint(cast(long)(round(z[i].re)))*basel;
            c[i] += Mint(cast(long)(round(z[i].im)))*baser;
        }
        basel *= Mint(1<<W);
        baser *= Mint(1<<W);
    }
    return c;
}

 


 

/* IMPORT /home/yosupo/Program/dcomp/source/dcomp/numeric/primitive.d */
// module dcomp.numeric.primitive;

import std.traits;
import std.bigint;

 
Unqual!T pow(T, U)(T x, U n)
if (!isFloatingPoint!T && (isIntegral!U || is(U == BigInt))) {
    return pow(x, n, T(1));
}

 
Unqual!T pow(T, U, V)(T x, U n, V e)
if ((isIntegral!U || is(U == BigInt)) && is(Unqual!T == Unqual!V)) {
    Unqual!T b = x, v = e;
    Unqual!U m = n;
    while (m) {
        if (m & 1) v *= b;
        b *= b;
        m /= 2;
    }
    return v;
}

 


T powMod(T, U, V)(T x, U n, V md)
if (isIntegral!U || is(U == BigInt)) {
    T r = T(1);
    while (n) {
        if (n & 1) r = (r*x)%md;
        x = (x*x)%md;
        n >>= 1;
    }
    return r % md;
}

ulong ulongPowMod(U)(ulong x, U n, ulong md)
if (isIntegral!U || is(U == BigInt)) {
//     import dcomp.int128;
    x %= md;
    ulong r = 1;
    while (n) {
        if (n & 1) {
            r = mul128(r, x).mod128(md);
        }
        x = mul128(x, x).mod128(md);
        n >>= 1;
    }
    return r % md;
}

 
T lcm(T)(in T a, in T b) {
    import std.numeric : gcd;
    return a / gcd(a,b) * b;
}

 
 

 
 
T[3] extGcd(T)(in T a, in T b) 
if (!isIntegral!T || isSigned!T)  
{
    if (b==0) {
        return [T(1), T(0), a];
    } else {
        auto e = extGcd(b, a%b);
        return [e[1], e[0]-a/b*e[1], e[2]];
    }
}

 
 
/* IMPORT /home/yosupo/Program/dcomp/source/dcomp/ldc/inline.d */
// module dcomp.ldc.inline;

version(LDC) {
    pragma(LDC_inline_ir)
        R inlineIR(string s, R, P...)(P);
}
/* IMPORT /home/yosupo/Program/dcomp/source/dcomp/scanner.d */
// module dcomp.scanner;

// import dcomp.container.stack;

 
class Scanner {
    import std.stdio : File;
    import std.conv : to;
    import std.range : front, popFront, array, ElementType;
    import std.array : split;
    import std.traits : isSomeChar, isStaticArray, isArray; 
    import std.algorithm : map;
    File f;
    this(File f) {
        this.f = f;
    }
    char[512] lineBuf;
    char[] line;
    private bool succW() {
        import std.range.primitives : empty, front, popFront;
        import std.ascii : isWhite;
        while (!line.empty && line.front.isWhite) {
            line.popFront;
        }
        return !line.empty;
    }
    private bool succ() {
        import std.range.primitives : empty, front, popFront;
        import std.ascii : isWhite;
        while (true) {
            while (!line.empty && line.front.isWhite) {
                line.popFront;
            }
            if (!line.empty) break;
            line = lineBuf[];
            f.readln(line);
            if (!line.length) return false;
        }
        return true;
    }

    private bool readSingle(T)(ref T x) {
        import std.algorithm : findSplitBefore;
        import std.string : strip;
        import std.conv : parse;
        if (!succ()) return false;
        static if (isArray!T) {
            alias E = ElementType!T;
            static if (isSomeChar!E) {
                 
                 
                auto r = line.findSplitBefore(" ");
                x = r[0].strip.dup;
                line = r[1];
            } else static if (isStaticArray!T) {
                foreach (i; 0..T.length) {
                    bool f = succW();
                    assert(f);
                    x[i] = line.parse!E;
                }
            } else {
                StackPayload!E buf;
                while (succW()) {
                    buf ~= line.parse!E;
                }
                x = buf.data;
            }
        } else {
            x = line.parse!T;
        }
        return true;
    }
    int read(T, Args...)(ref T x, auto ref Args args) {
        if (!readSingle(x)) return 0;
        static if (args.length == 0) {
            return 1;
        } else {
            return 1 + read(args);
        }
    }
}


 
 

 
/* IMPORT /home/yosupo/Program/dcomp/source/dcomp/foundation.d */
// module dcomp.foundation;
 
static if (__VERSION__ <= 2070) {
    /*
    Copied by https://github.com/dlang/phobos/blob/master/std/algorithm/iteration.d
    Copyright: Andrei Alexandrescu 2008-.
    License: $(HTTP boost.org/LICENSE_1_0.txt, Boost License 1.0).
    */
    template fold(fun...) if (fun.length >= 1) {
        auto fold(R, S...)(R r, S seed) {
            import std.algorithm : reduce;
            static if (S.length < 2) {
                return reduce!fun(seed, r);
            } else {
                import std.typecons : tuple;
                return reduce!fun(tuple(seed), r);
            }
        }
    }
     
}

import core.bitop : popcnt;
static if (!__traits(compiles, popcnt(ulong.max))) {
    public import core.bitop : popcnt;
    int popcnt(ulong v) {
        return popcnt(cast(uint)(v)) + popcnt(cast(uint)(v>>32));
    }
}

bool poppar(ulong v) {
    v^=v>>1;
    v^=v>>2;
    v&=0x1111111111111111UL;
    v*=0x1111111111111111UL;
    return ((v>>60) & 1) != 0;
}
/* IMPORT /home/yosupo/Program/dcomp/source/dcomp/container/stack.d */
// module dcomp.container.stack;

struct StackPayload(T, size_t MIN = 4) {
    import core.exception : RangeError;
    import std.algorithm : max;
    import std.conv;
    import std.range.primitives : ElementEncodingType;
    import core.stdc.string : memcpy;

    private T* _data;
    private uint len, cap;
     
    bool empty() const { return len == 0; }
    @property size_t length() const { return len; }
    alias opDollar = length;

    ref inout(T) opIndex(size_t i) inout { return _data[i]; }
    ref inout(T) front() inout { return _data[0]; }
    ref inout(T) back() inout { assert(len); return _data[len-1]; }
    
     
    void reserve(size_t nlen) {
        import core.memory : GC;
        if (nlen <= cap) return;
        
        void* nx = GC.malloc(nlen * T.sizeof);

        cap = nlen.to!uint;
        if (len) memcpy(nx, _data, len * T.sizeof);
        _data = cast(T*)(nx);
    }
    void free() {
        import core.memory : GC;
        GC.free(_data);
    }
     
    void opOpAssign(string op : "~")(T item) {
        if (len == cap) {
            reserve(max(MIN, cap*2));
        }
        _data[len++] = item;
    }
     
    void insertBack(T item) {
        this ~= item;
    }
     
    void removeBack() {
        len--;
    }
     
    void clear() {
        len = 0;
    }
     
    inout(T)[] data() inout {
        return (_data) ? _data[0..len] : null;
    }

    static struct RangeT(A) {
        import std.traits : CopyTypeQualifiers;
        alias E = CopyTypeQualifiers!(A, T);
        A *p;
        size_t a, b;
        @property bool empty() const { return b <= a; }
        @property size_t length() const { return b-a; }
        @property RangeT save() { return RangeT(p, a, b); }
        @property RangeT!(const A) save() const {
            return typeof(return)(p, a, b);
        }
        alias opDollar = length;
        @property ref inout(E) front() inout { return (*p)[a]; }
        @property ref inout(E) back() inout { return (*p)[b-1]; }
        void popFront() {
            version(assert) if (empty) throw new RangeError();
            a++;
        }
        void popBack() {
            version(assert) if (empty) throw new RangeError();
            b--;
        }
        ref inout(E) opIndex(size_t i) inout { return (*p)[i]; }
        RangeT opSlice() { return this.save; }
        RangeT opSlice(size_t i, size_t j) {
            version(assert) if (i > j || a + j > b) throw new RangeError();
            return typeof(return)(p, a+i, a+j);
        }
        RangeT!(const A) opSlice() const { return this.save; }
        RangeT!(const A) opSlice(size_t i, size_t j) const {
            version(assert) if (i > j || a + j > b) throw new RangeError();
            return typeof(return)(p, a+i, a+j);
        }
    }
    alias Range = RangeT!(StackPayload!T);
    alias ConstRange = RangeT!(const StackPayload!T);
    alias ImmutableRange = RangeT!(immutable StackPayload!T);
}

 

struct Stack(T) {
    import core.exception : RangeError;
    import core.memory : GC;
    import std.range : ElementType, isInputRange;
    import std.traits : isImplicitlyConvertible;

    alias Payload = StackPayload!T;
    alias Range = Payload.Range;
    alias ConstRange = Payload.ConstRange;
    alias ImmutableRange = Payload.ImmutableRange;
    
    Payload* p;
    private void I() { if (!p) p = new Payload(); }
    private void C() const {
        version(assert) if (!p) throw new RangeError();
    }
     
    private this(Payload* p) {
        this.p = p;
    }
    this(U)(U[] values...) if (isImplicitlyConvertible!(U, T)) {
        p = new Payload();
        foreach (v; values) {
            insertBack(v);
        }
    }
     
    this(Range)(Range r)
    if (isInputRange!Range &&
    isImplicitlyConvertible!(ElementType!Range, T) &&
    !is(Range == T[])) {
        p = new Payload();
        foreach (v; r) {
            insertBack(v);
        }
    }
    static Stack make() { return Stack(new Payload()); }
    @property bool havePayload() const { return (p !is null); }
     
    @property bool empty() const { return (!havePayload || p.empty); }
     
    @property size_t length() const { return (havePayload ? p.length : 0); }
    @property inout(T)[] data() inout {C; return (!p) ? [] : p.data; }
     
    alias opDollar = length;
    ref inout(T) opIndex(size_t i) inout {C; return (*p)[i]; }
     
    ref inout(T) front() inout {C; return (*p)[0]; }
     
    ref inout(T) back() inout {C; return (*p)[$-1]; }
    void clear() { if (p) p.clear(); }
     
    void insertBack(T v) {I; p.insertBack(v); }
     
    alias stableInsertBack = insertBack;
     
    void removeBack() {C; p.removeBack(); }
     
    Range opSlice() {I; return Range(p, 0, length); }
}

 
 
/* IMPORT /home/yosupo/Program/dcomp/source/dcomp/int128.d */
 

// module dcomp.int128;

// import dcomp.array;

version(LDC) {
//     import dcomp.ldc.inline;
}

version(LDC) version(X86_64) {
    version = LDC_IR;
}

 
ulong[2] mul128(ulong a, ulong b) {
    ulong[2] res;
    version(LDC_IR) {
        ulong upper, lower;
        inlineIR!(`
            %r0 = zext i64 %0 to i128 
            %r1 = zext i64 %1 to i128
            %r2 = mul i128 %r1, %r0
            %r3 = trunc i128 %r2 to i64
            %r4 = lshr i128 %r2, 64
            %r5 = trunc i128 %r4 to i64
            store i64 %r3, i64* %2
            store i64 %r5, i64* %3`, void)(a, b, &lower, &upper);
        return [lower, upper];
    } else version(D_InlineAsm_X86_64) {
        ulong upper, lower;
        asm {
            mov RAX, a;
            mul b;
            mov lower, RAX;
            mov upper, RDX;
        }
        return [lower, upper];
    } else {
        ulong B = 2UL^^32;
        ulong[2] a2 = [a % B, a / B];
        ulong[2] b2 = [b % B, b / B];
        ulong[4] c;
        foreach (i; 0..2) {
            foreach (j; 0..2) {
                c[i+j] += a2[i] * b2[j] % B;
                c[i+j+1] += a2[i] * b2[j] / B;
            }
        }
        foreach (i; 0..3) {
            c[i+1] += c[i] / B;
            c[i] %= B;
        }
        return [c[0] + c[1] * B, c[2] + c[3] * B];
    }
}

 

 
ulong div128(ulong[2] a, ulong b) {
    version(LDC_IR) {
        return inlineIR!(`
            %r0 = zext i64 %0 to i128
            %r1 = zext i64 %1 to i128
            %r2 = shl i128 %r1, 64
            %r3 = add i128 %r0, %r2
            %r4 = zext i64 %2 to i128
            %r5 = udiv i128 %r3, %r4
            %r6 = trunc i128 %r5 to i64
            ret i64 %r6`,ulong)(a[0], a[1], b);
    } else version(D_InlineAsm_X86_64) {
        ulong upper = a[1], lower = a[0];
        ulong res;
        asm {
            mov RDX, upper;
            mov RAX, lower;
            div b;
            mov res, RAX;
        }
        return res;
    } else {
        if (b == 1) return a[0];
        while (!(b & (1UL << 63))) {
            a[1] <<= 1;
            if (a[0] & (1UL << 63)) a[1] |= 1;
            a[0] <<= 1;
            b <<= 1;
        }
        ulong ans = 0;
        foreach (i; 0..64) {
            bool up = (a[1] & (1UL << 63)) != 0;
            a[1] <<= 1;
            if (a[0] & (1UL << 63)) a[1] |= 1;
            a[0] <<= 1;

            ans <<= 1;
            if (up || b <= a[1]) {
                a[1] -= b;
                ans++;
            }
        }
        return ans;
    }
}


 
ulong mod128(ulong[2] a, ulong b) {
    version(D_InlineAsm_X86_64) {
        ulong upper = a[1], lower = a[0];
        ulong res;
        asm {
            mov RDX, upper;
            mov RAX, lower;
            div b;
            mov res, RDX;
        }
        return res;
    } else {
        return a[0] - div128(a, b) * b;
    }
}

 
/* IMPORT /home/yosupo/Program/dcomp/source/dcomp/array.d */
// module dcomp.array;

 
T[N] fixed(T, size_t N)(T[N] a) {return a;}

 
 

/*
This source code generated by dcomp and include dcomp's source code.
dcomp's Copyright: Copyright (c) 2016- Kohei Morita. (https://github.com/yosupo06/dcomp)
dcomp's License: MIT License(https://github.com/yosupo06/dcomp/blob/master/LICENSE.txt)
*/
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