/
005.cr
190 lines (155 loc) · 2.86 KB
/
005.cr
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struct Mint
MOD = 1000000007i64
def self.zero
new
end
def self.raw(value : Int64)
result = new
result.value = value
result
end
@value : Int64
def initialize
@value = 0i64
end
def initialize(value)
@value = value.to_i64 % MOD
end
def initialize(m : self)
@value = m.value
end
protected def value=(value : Int64)
@value = value
end
getter value : Int64
def + : self
self
end
def - : self
Mint.raw(value != 0 ? MOD &- value : 0i64)
end
def +(v)
self + v.to_m
end
def +(m : self)
x = value &+ m.value
x &-= MOD if x >= MOD
Mint.raw(x)
end
def -(v)
self - v.to_m
end
def -(m : self)
x = value &- m.value
x &+= MOD if x < 0
Mint.raw(x)
end
def *(v)
self * v.to_m
end
def *(m : self)
Mint.new(value &* m.value)
end
def /(v)
self / v.to_m
end
def /(m : self)
raise DivisionByZeroError.new if m.value == 0
a, b, u, v = m.to_i64, MOD, 1i64, 0i64
while b != 0
t = a // b
a &-= t &* b
a, b = b, a
u &-= t &* v
u, v = v, u
end
Mint.new(value &* u)
end
def //(v)
self / v
end
def **(exponent : Int)
t, res = self, Mint.raw(1i64)
while exponent > 0
res *= t if exponent & 1 == 1
t *= t
exponent >>= 1
end
res
end
def ==(m : self)
value == m.value
end
def ==(m : Int)
raise NotImplementedError.new("==")
end
def succ
Mint.raw(value != MOD &- 1 ? value &+ 1 : 0i64)
end
def pred
Mint.raw(value != 0 ? value &- 1 : MOD &- 1)
end
def abs
self
end
def to_i64 : Int64
value
end
delegate to_s, to: @value
delegate inspect, to: @value
end
struct Int
{% for op in %w[+ - * / //] %}
def {{op.id}}(value : Mint)
to_m {{op.id}} value
end
{% end %}
def to_m : Mint
Mint.new(self)
end
end
class String
def to_m : Mint
Mint.new(self)
end
end
struct Int
def powmod(exp : T, mod : self) forall T
n = self % mod
res = typeof(self).new(1)
while exp > 0
res = res * n % mod if exp.odd?
n = n * n % mod
exp >>= 1
end
res
end
end
n, b, k = read_line.split.try { |(n, b, k)|
{n.to_i64, b.to_i, k.to_i}
}
a = read_line.split.map(&.to_i)
m = Math.log2(n).ceil.to_i + 1
dp_marge = ->(dp1 : Array(Mint), digit : Int64, dp2 : Array(Mint)) {
dp_res = Array.new(b, Mint.zero)
pow10 = 10.powmod(digit, b)
(0...b).each do |i|
(0...b).each do |j|
dp_res[(i * pow10 + j) % b] += dp1[i] * dp2[j]
end
end
dp_res
}
doubling = Array.new(1) { [Mint.zero] * b }
a.each { |j|
doubling[0][j % b] += 1
}
(1..m).each { |i|
doubling << dp_marge.call(doubling[-1], 2i64**i.pred, doubling[-1])
}
dp = [Mint.zero] * b
dp[0] = 1.to_m
(0..m).select { |i| n.bit(i) == 1 }.each do |i|
dp = dp_marge.call(dp, 2i64**i, doubling[i])
end
puts dp[0]