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467 lines (460 loc) · 16.4 KB
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/**
* @verified
* <ul>
* <li> https://atcoder.jp/contests/arc050/tasks/arc050_c
* <li> https://atcoder.jp/contests/abc129/tasks/abc129_f
* </ul>
*/
class ModIntFactory {
private final ModArithmetic ma;
private final int mod;
public ModIntFactory(int mod) {
this.ma = ModArithmetic.of(mod);
this.mod = mod;
}
public ModInt create(long value) {
if ((value %= mod) < 0) value += mod;
if (ma instanceof ModArithmetic.ModArithmeticMontgomery) {
return new ModInt(((ModArithmetic.ModArithmeticMontgomery) ma).generate(value));
}
return new ModInt((int) value);
}
class ModInt {
private int value;
private ModInt(int value) {
this.value = value;
}
public int mod() {
return mod;
}
public int value() {
if (ma instanceof ModArithmetic.ModArithmeticMontgomery) {
return ((ModArithmetic.ModArithmeticMontgomery) ma).reduce(value);
}
return value;
}
public ModInt add(ModInt mi) {
return new ModInt(ma.add(value, mi.value));
}
public ModInt add(ModInt mi1, ModInt mi2) {
return new ModInt(ma.add(value, mi1.value)).addAsg(mi2);
}
public ModInt add(ModInt mi1, ModInt mi2, ModInt mi3) {
return new ModInt(ma.add(value, mi1.value)).addAsg(mi2).addAsg(mi3);
}
public ModInt add(ModInt mi1, ModInt mi2, ModInt mi3, ModInt mi4) {
return new ModInt(ma.add(value, mi1.value)).addAsg(mi2).addAsg(mi3).addAsg(mi4);
}
public ModInt add(ModInt mi1, ModInt... mis) {
ModInt mi = add(mi1);
for (ModInt m : mis) mi.addAsg(m);
return mi;
}
public ModInt add(long mi) {
return new ModInt(ma.add(value, ma.remainder(mi)));
}
public ModInt sub(ModInt mi) {
return new ModInt(ma.sub(value, mi.value));
}
public ModInt sub(long mi) {
return new ModInt(ma.sub(value, ma.remainder(mi)));
}
public ModInt mul(ModInt mi) {
return new ModInt(ma.mul(value, mi.value));
}
public ModInt mul(ModInt mi1, ModInt mi2) {
return new ModInt(ma.mul(value, mi1.value)).mulAsg(mi2);
}
public ModInt mul(ModInt mi1, ModInt mi2, ModInt mi3) {
return new ModInt(ma.mul(value, mi1.value)).mulAsg(mi2).mulAsg(mi3);
}
public ModInt mul(ModInt mi1, ModInt mi2, ModInt mi3, ModInt mi4) {
return new ModInt(ma.mul(value, mi1.value)).mulAsg(mi2).mulAsg(mi3).mulAsg(mi4);
}
public ModInt mul(ModInt mi1, ModInt... mis) {
ModInt mi = mul(mi1);
for (ModInt m : mis) mi.mulAsg(m);
return mi;
}
public ModInt mul(long mi) {
return new ModInt(ma.mul(value, ma.remainder(mi)));
}
public ModInt div(ModInt mi) {
return new ModInt(ma.div(value, mi.value));
}
public ModInt div(long mi) {
return new ModInt(ma.div(value, ma.remainder(mi)));
}
public ModInt inv() {
return new ModInt(ma.inv(value));
}
public ModInt pow(long b) {
return new ModInt(ma.pow(value, b));
}
public ModInt addAsg(ModInt mi) {
this.value = ma.add(value, mi.value);
return this;
}
public ModInt addAsg(ModInt mi1, ModInt mi2) {
return addAsg(mi1).addAsg(mi2);
}
public ModInt addAsg(ModInt mi1, ModInt mi2, ModInt mi3) {
return addAsg(mi1).addAsg(mi2).addAsg(mi3);
}
public ModInt addAsg(ModInt mi1, ModInt mi2, ModInt mi3, ModInt mi4) {
return addAsg(mi1).addAsg(mi2).addAsg(mi3).addAsg(mi4);
}
public ModInt addAsg(ModInt... mis) {
for (ModInt m : mis) addAsg(m);
return this;
}
public ModInt addAsg(long mi) {
this.value = ma.add(value, ma.remainder(mi));
return this;
}
public ModInt subAsg(ModInt mi) {
this.value = ma.sub(value, mi.value);
return this;
}
public ModInt subAsg(long mi) {
this.value = ma.sub(value, ma.remainder(mi));
return this;
}
public ModInt mulAsg(ModInt mi) {
this.value = ma.mul(value, mi.value);
return this;
}
public ModInt mulAsg(ModInt mi1, ModInt mi2) {
return mulAsg(mi1).mulAsg(mi2);
}
public ModInt mulAsg(ModInt mi1, ModInt mi2, ModInt mi3) {
return mulAsg(mi1).mulAsg(mi2).mulAsg(mi3);
}
public ModInt mulAsg(ModInt mi1, ModInt mi2, ModInt mi3, ModInt mi4) {
return mulAsg(mi1).mulAsg(mi2).mulAsg(mi3).mulAsg(mi4);
}
public ModInt mulAsg(ModInt... mis) {
for (ModInt m : mis) mulAsg(m);
return this;
}
public ModInt mulAsg(long mi) {
this.value = ma.mul(value, ma.remainder(mi));
return this;
}
public ModInt divAsg(ModInt mi) {
this.value = ma.div(value, mi.value);
return this;
}
public ModInt divAsg(long mi) {
this.value = ma.div(value, ma.remainder(mi));
return this;
}
@Override
public String toString() {
return String.valueOf(value());
}
@Override
public boolean equals(Object o) {
if (o instanceof ModInt) {
ModInt mi = (ModInt) o;
return mod() == mi.mod() && value() == mi.value();
}
return false;
}
@Override
public int hashCode() {
return (1 * 37 + mod()) * 37 + value();
}
}
private interface ModArithmetic {
public int mod();
public int remainder(long value);
public int add(int a, int b);
public int sub(int a, int b);
public int mul(int a, int b);
public default int div(int a, int b) {
return mul(a, inv(b));
}
public int inv(int a);
public int pow(int a, long b);
public static ModArithmetic of(int mod) {
if (mod <= 0) {
throw new IllegalArgumentException();
} else if (mod == 1) {
return new ModArithmetic1();
} else if (mod == 2) {
return new ModArithmetic2();
} else if (mod == 998244353) {
return new ModArithmetic998244353();
} else if (mod == 1000000007) {
return new ModArithmetic1000000007();
} else if ((mod & 1) == 1) {
return new ModArithmeticMontgomery(mod);
} else {
return new ModArithmeticBarrett(mod);
}
}
static final class ModArithmetic1 implements ModArithmetic {
public int mod() {return 1;}
public int remainder(long value) {return 0;}
public int add(int a, int b) {return 0;}
public int sub(int a, int b) {return 0;}
public int mul(int a, int b) {return 0;}
public int inv(int a) {throw new ArithmeticException("divide by zero");}
public int pow(int a, long b) {return 0;}
}
static final class ModArithmetic2 implements ModArithmetic {
public int mod() {return 2;}
public int remainder(long value) {return (int) (value & 1);}
public int add(int a, int b) {return a ^ b;}
public int sub(int a, int b) {return a ^ b;}
public int mul(int a, int b) {return a & b;}
public int inv(int a) {
if (a == 0) throw new ArithmeticException("divide by zero");
return a;
}
public int pow(int a, long b) {
if (b == 0) return 1;
return a;
}
}
static final class ModArithmetic998244353 implements ModArithmetic {
private final int mod = 998244353;
public int mod() {
return mod;
}
public int remainder(long value) {
return (int) ((value %= mod) < 0 ? value + mod : value);
}
public int add(int a, int b) {
int res = a + b;
return res >= mod ? res - mod : res;
}
public int sub(int a, int b) {
int res = a - b;
return res < 0 ? res + mod : res;
}
public int mul(int a, int b) {
return (int) (((long) a * b) % mod);
}
public int inv(int a) {
int b = mod;
long u = 1, v = 0;
while (b >= 1) {
long t = a / b;
a -= t * b;
int tmp1 = a; a = b; b = tmp1;
u -= t * v;
long tmp2 = u; u = v; v = tmp2;
}
u %= mod;
if (a != 1) {
throw new ArithmeticException("divide by zero");
}
return (int) (u < 0 ? u + mod : u);
}
public int pow(int a, long b) {
if (b < 0) throw new ArithmeticException("negative power");
long res = 1;
long pow2 = a;
long idx = 1;
while (b > 0) {
long lsb = b & -b;
for (; lsb != idx; idx <<= 1) {
pow2 = (pow2 * pow2) % mod;
}
res = (res * pow2) % mod;
b ^= lsb;
}
return (int) res;
}
}
static final class ModArithmetic1000000007 implements ModArithmetic {
private final int mod = 1000000007;
public int mod() {
return mod;
}
public int remainder(long value) {
return (int) ((value %= mod) < 0 ? value + mod : value);
}
public int add(int a, int b) {
int res = a + b;
return res >= mod ? res - mod : res;
}
public int sub(int a, int b) {
int res = a - b;
return res < 0 ? res + mod : res;
}
public int mul(int a, int b) {
return (int) (((long) a * b) % mod);
}
public int div(int a, int b) {
return mul(a, inv(b));
}
public int inv(int a) {
int b = mod;
long u = 1, v = 0;
while (b >= 1) {
long t = a / b;
a -= t * b;
int tmp1 = a; a = b; b = tmp1;
u -= t * v;
long tmp2 = u; u = v; v = tmp2;
}
u %= mod;
if (a != 1) {
throw new ArithmeticException("divide by zero");
}
return (int) (u < 0 ? u + mod : u);
}
public int pow(int a, long b) {
if (b < 0) throw new ArithmeticException("negative power");
long res = 1;
long pow2 = a;
long idx = 1;
while (b > 0) {
long lsb = b & -b;
for (; lsb != idx; idx <<= 1) {
pow2 = (pow2 * pow2) % mod;
}
res = (res * pow2) % mod;
b ^= lsb;
}
return (int) res;
}
}
static final class ModArithmeticMontgomery extends ModArithmeticDynamic {
private final long negInv;
private final long r2, r3;
private ModArithmeticMontgomery(int mod) {
super(mod);
long inv = 0;
long s = 1, t = 0;
for (int i = 0; i < 32; i++) {
if ((t & 1) == 0) {
t += mod;
inv += s;
}
t >>= 1;
s <<= 1;
}
long r = (1l << 32) % mod;
this.negInv = inv;
this.r2 = (r * r) % mod;
this.r3 = (r2 * r) % mod;
}
private int generate(long x) {
return reduce(x * r2);
}
private int reduce(long x) {
x = (x + ((x * negInv) & 0xffff_ffffl) * mod) >>> 32;
return (int) (x < mod ? x : x - mod);
}
@Override
public int remainder(long value) {
return generate((value %= mod) < 0 ? value + mod : value);
}
@Override
public int mul(int a, int b) {
return reduce((long) a * b);
}
@Override
public int inv(int a) {
a = super.inv(a);
return reduce(a * r3);
}
@Override
public int pow(int a, long b) {
return generate(super.pow(a, b));
}
}
static final class ModArithmeticBarrett extends ModArithmeticDynamic {
private static final long mask = 0xffff_ffffl;
private final long mh;
private final long ml;
private ModArithmeticBarrett(int mod) {
super(mod);
/**
* m = floor(2^64/mod)
* 2^64 = p*mod + q, 2^32 = a*mod + b
* => (a*mod + b)^2 = p*mod + q
* => p = mod*a^2 + 2ab + floor(b^2/mod)
*/
long a = (1l << 32) / mod;
long b = (1l << 32) % mod;
long m = a * a * mod + 2 * a * b + (b * b) / mod;
mh = m >>> 32;
ml = m & mask;
}
private int reduce(long x) {
long z = (x & mask) * ml;
z = (x & mask) * mh + (x >>> 32) * ml + (z >>> 32);
z = (x >>> 32) * mh + (z >>> 32);
x -= z * mod;
return (int) (x < mod ? x : x - mod);
}
@Override
public int remainder(long value) {
return (int) ((value %= mod) < 0 ? value + mod : value);
}
@Override
public int mul(int a, int b) {
return reduce((long) a * b);
}
}
static class ModArithmeticDynamic implements ModArithmetic {
final int mod;
public ModArithmeticDynamic(int mod) {
this.mod = mod;
}
public int mod() {
return mod;
}
public int remainder(long value) {
return (int) ((value %= mod) < 0 ? value + mod : value);
}
public int add(int a, int b) {
int sum = a + b;
return sum >= mod ? sum - mod : sum;
}
public int sub(int a, int b) {
int sum = a - b;
return sum < 0 ? sum + mod : sum;
}
public int mul(int a, int b) {
return (int) (((long) a * b) % mod);
}
public int inv(int a) {
int b = mod;
long u = 1, v = 0;
while (b >= 1) {
long t = a / b;
a -= t * b;
int tmp1 = a; a = b; b = tmp1;
u -= t * v;
long tmp2 = u; u = v; v = tmp2;
}
u %= mod;
if (a != 1) {
throw new ArithmeticException("divide by zero");
}
return (int) (u < 0 ? u + mod : u);
}
public int pow(int a, long b) {
if (b < 0) throw new ArithmeticException("negative power");
int res = 1;
int pow2 = a;
long idx = 1;
while (b > 0) {
long lsb = b & -b;
for (; lsb != idx; idx <<= 1) {
pow2 = mul(pow2, pow2);
}
res = mul(res, pow2);
b ^= lsb;
}
return res;
}
}
}
}
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