#![allow(unused_imports, non_snake_case)]
#![allow(dead_code)]
use crate::scanner::Scanner;
use crate::{data_structure::segment_tree::SegRangeAdd, query::imosm::imos};
modint!();
fn main() {
    let mut scan = Scanner::new();
    let n = scan.read::<i32>();
    let d = scan.read::<i32>();
    let k = scan.read::<i32>();
    let mut dp = list ! ( Z :: new ( 0 ) ; d * n + 1 );
    dp[0] = Z::new(1);
    for _ in 0..n {
        let mut ranges = list!();
        for i in 0..=d * n {
            let x = dp[i];
            if i + 1 < dp.ilen() {
                ranges.push((i + 1..=i + d, x));
            }
        }
        dp = imos(dp.ilen(), &ranges);
    }
    println!("{}", dp[k]);
}
pub mod data_structure {
    pub mod segment_tree {
        use crate::ext::range::{IntRangeBounds, RangeEx};
        use crate::{arraylist::List, independent::integer::Int};
        use std::ops::{Range, RangeBounds};
        pub struct SegTree<'a> {
            node: List<i64>,
            op: Box<dyn Fn(i64, i64) -> i64 + 'a>,
            zero: i64,
            n: i32,
        }
        impl<'a> SegTree<'a> {
            pub fn new<B>(v: List<i64>, zero: i64, op: B) -> SegTree<'a>
            where
                B: Fn(i64, i64) -> i64 + 'a,
            {
                let size = v.ilen();
                let mut n = 1i32;
                while n < size {
                    n *= 2
                }
                let mut node = List::init(zero, 2 * n - 1);
                for i in 0..size {
                    node[i + n - 1] = v[i]
                }
                for i in (0..n - 1).rev() {
                    node[i] = op(node[2 * i + 1], node[2 * i + 2])
                }
                SegTree {
                    node,
                    op: Box::new(op),
                    zero,
                    n,
                }
            }
            pub fn set(&mut self, mut x: i32, value: i64) {
                x += self.n - 1;
                self.node[x] = value;
                while x > 0 {
                    x = (x - 1) / 2;
                    self.node[x] = (self.op)(self.node[2 * x + 1], self.node[2 * x + 2]);
                }
            }
            pub fn get1(&self, i: i32) -> i64 {
                self.getrec(i..i + 1, 0, 0..self.n)
            }
            pub fn get<T>(&self, query: T) -> i64
            where
                T: RangeBounds<i32>,
            {
                self.getrec(query.to_harfopen(0, self.n), 0, 0..self.n)
            }
            fn getrec(&self, query: Range<i32>, k: i32, range: Range<i32>) -> i64 {
                if query.separate_range(&range) {
                    return self.zero;
                }
                if query.contain_range(&range) {
                    return self.node[k];
                }
                let vl = self.getrec(
                    query.clone(),
                    2 * k + 1,
                    range.start..(range.start + range.end) / 2,
                );
                let vr = self.getrec(
                    query.clone(),
                    2 * k + 2,
                    (range.start + range.end) / 2..range.end,
                );
                (self.op)(vl, vr)
            }
        }
        pub struct DualSegTree<'a> {
            node: List<i64>,
            op: Box<dyn Fn(i64, i64) -> i64 + 'a>,
            n: i32,
        }
        impl<'a> DualSegTree<'a> {
            pub fn new<B>(v: List<i64>, zero: i64, op: B) -> DualSegTree<'a>
            where
                B: Fn(i64, i64) -> i64 + 'a,
            {
                let size = v.ilen();
                let mut n = 1i32;
                while n < size {
                    n *= 2
                }
                let mut node = List::init(zero, 2 * n - 1);
                for i in 0..size {
                    node[i + n - 1] = v[i]
                }
                for i in (0..n - 1).rev() {
                    node[i] = op(node[2 * i + 1], node[2 * i + 2])
                }
                DualSegTree {
                    node,
                    op: Box::new(op),
                    n,
                }
            }
            pub fn get(&self, mut x: i32) -> i64 {
                x += self.n - 1;
                let mut ret = self.node[x];
                while x > 0 {
                    x = (x - 1) / 2;
                    ret = (self.op)(ret, self.node[x]);
                }
                ret
            }
            pub fn set<T>(&mut self, query: T, value: i64)
            where
                T: RangeBounds<i32>,
            {
                let n = self.n;
                self.setrec(query.to_harfopen(0, n), 0, 0..n, value);
            }
            fn setrec(&mut self, query: Range<i32>, k: i32, range: Range<i32>, value: i64) {
                if query.separate_range(&range) {
                    return;
                }
                if query.contain_range(&range) {
                    self.node[k] = (self.op)(self.node[k], value);
                    return;
                }
                self.setrec(
                    query.clone(),
                    2 * k + 1,
                    range.start..(range.start + range.end) / 2,
                    value,
                );
                self.setrec(
                    query.clone(),
                    2 * k + 2,
                    (range.start + range.end) / 2..range.end,
                    value,
                );
            }
        }
        pub struct SegRangeAdd<T> {
            node: List<T>,
            lazy: List<T>,
            n: i32,
        }
        impl<T: Int> SegRangeAdd<T> {
            pub fn new(v: List<T>) -> SegRangeAdd<T> {
                let size = v.ilen();
                let mut n = 1;
                while n < size {
                    n *= 2
                }
                let mut node = List::init(T::zero(), 2 * n - 1);
                let lazy = List::init(T::zero(), 2 * n - 1);
                for i in 0..size {
                    node[i + n - 1] = v[i]
                }
                for i in (0..n - 1).rev() {
                    node[i] = node[i * 2 + 1] + node[i * 2 + 2]
                }
                SegRangeAdd { node, lazy, n }
            }
            fn eval(&mut self, k: i32, range: Range<i32>) {
                if self.lazy[k] != T::zero() {
                    let tmp = self.lazy[k];
                    self.node[k] += tmp;
                    if range.width() > 1 {
                        self.lazy[2 * k + 1] += tmp / T::one().next();
                        self.lazy[2 * k + 2] += tmp / T::one().next();
                    }
                    self.lazy[k] = T::zero();
                }
            }
            pub fn add<U>(&mut self, query: U, x: T)
            where
                U: RangeBounds<i32>,
            {
                let n = self.n;
                self.addrec(query.to_harfopen(0, n), x, 0, 0..n)
            }
            fn addrec(&mut self, query: Range<i32>, x: T, k: i32, range: Range<i32>) {
                self.eval(k, range.clone());
                if query.separate_range(&range) {
                    return;
                }
                if query.contain_range(&range) {
                    self.lazy[k] += T::from_i32(range.width()) * x;
                    self.eval(k, range.clone());
                } else {
                    self.addrec(
                        query.clone(),
                        x,
                        2 * k + 1,
                        range.start..(range.start + range.end) / 2,
                    );
                    self.addrec(
                        query.clone(),
                        x,
                        2 * k + 2,
                        (range.start + range.end) / 2..range.end,
                    );
                    self.node[k] = self.node[2 * k + 1] + self.node[2 * k + 2];
                }
            }
            pub fn sum<U>(&mut self, query: U) -> T
            where
                U: RangeBounds<i32>,
            {
                let n = self.n;
                self.sumrec(query.to_harfopen(0, n), 0, 0..n)
            }
            fn sumrec(&mut self, query: Range<i32>, k: i32, range: Range<i32>) -> T {
                if query.separate_range(&range) {
                    return T::zero();
                }
                self.eval(k, range.clone());
                if query.contain_range(&range) {
                    return self.node[k];
                }
                let vl = self.sumrec(
                    query.clone(),
                    2 * k + 1,
                    range.start..(range.start + range.end) / 2,
                );
                let vr = self.sumrec(
                    query.clone(),
                    2 * k + 2,
                    (range.start + range.end) / 2..range.end,
                );
                vl + vr
            }
        }
        pub struct SegRangeUpdate<'a> {
            node: List<i64>,
            lazy: List<i64>,
            has_lazy: List<bool>,
            op: Box<dyn Fn(i64, i64) -> i64 + 'a>,
            zero: i64,
            n: i32,
        }
        impl<'a> SegRangeUpdate<'a> {
            pub fn new<B>(v: List<i64>, zero: i64, op: B) -> SegRangeUpdate<'a>
            where
                B: Fn(i64, i64) -> i64 + 'a,
            {
                let size = v.ilen();
                let mut n = 1i32;
                while n < size {
                    n *= 2
                }
                let mut node = List::init(zero, 2 * n - 1);
                let lazy = List::init(0, 2 * n - 1);
                let has_lazy = List::init(false, 2 * n - 1);
                for i in 0..size {
                    node[i + n - 1] = v[i]
                }
                for i in (0..n - 1).rev() {
                    node[i] = op(node[i * 2 + 1], node[i * 2 + 2])
                }
                SegRangeUpdate {
                    node,
                    lazy,
                    has_lazy,
                    op: Box::new(op),
                    zero,
                    n,
                }
            }
            fn eval(&mut self, k: i32, range: Range<i32>) {
                if self.has_lazy[k] {
                    self.node[k] = self.lazy[k];
                    if range.width() > 1 {
                        self.lazy[2 * k + 1] = self.lazy[k];
                        self.lazy[2 * k + 2] = self.lazy[k];
                        self.has_lazy[2 * k + 1] = true;
                        self.has_lazy[2 * k + 2] = true;
                    }
                    self.has_lazy[k] = false;
                }
            }
            pub fn set<T>(&mut self, query: T, x: i64)
            where
                T: RangeBounds<i32>,
            {
                let n = self.n;
                self.setrec(query.to_harfopen(0, n), x, 0, 0..n)
            }
            fn setrec(&mut self, query: Range<i32>, x: i64, k: i32, range: Range<i32>) {
                self.eval(k, range.clone());
                if query.separate_range(&range) {
                    return;
                }
                if query.contain_range(&range) {
                    self.lazy[k] = x;
                    self.has_lazy[k] = true;
                    self.eval(k, range.clone());
                } else {
                    self.setrec(
                        query.clone(),
                        x,
                        2 * k + 1,
                        range.start..(range.start + range.end) / 2,
                    );
                    self.setrec(
                        query.clone(),
                        x,
                        2 * k + 2,
                        (range.start + range.end) / 2..range.end,
                    );
                    self.node[k] = (self.op)(self.node[2 * k + 1], self.node[2 * k + 2]);
                }
            }
            pub fn get<T>(&mut self, query: T) -> i64
            where
                T: RangeBounds<i32>,
            {
                let n = self.n;
                self.getrec(query.to_harfopen(0, n), 0, 0..n)
            }
            fn getrec(&mut self, query: Range<i32>, k: i32, range: Range<i32>) -> i64 {
                if query.separate_range(&range) {
                    return self.zero;
                }
                self.eval(k, range.clone());
                if query.contain_range(&range) {
                    return self.node[k];
                }
                let vl = self.getrec(
                    query.clone(),
                    2 * k + 1,
                    range.start..(range.start + range.end) / 2,
                );
                let vr = self.getrec(
                    query.clone(),
                    2 * k + 2,
                    (range.start + range.end) / 2..range.end,
                );
                (self.op)(vl, vr)
            }
        }
        pub struct SegIndexTree<'a> {
            node: List<(i64, i32)>,
            zero: i64,
            op: Box<dyn Fn((i64, i32), (i64, i32)) -> (i64, i32) + 'a>,
            n: i32,
        }
        impl<'a> SegIndexTree<'a> {
            pub fn new<B>(v: List<i64>, zero: i64, op: B) -> SegIndexTree<'a>
            where
                B: Fn((i64, i32), (i64, i32)) -> (i64, i32) + 'a,
            {
                let size = v.ilen();
                let mut n = 1i32;
                while n < size {
                    n *= 2
                }
                let mut node = List::init((zero, 0), 2 * n - 1);
                for i in 0..size {
                    node[i + n - 1] = (v[i], i)
                }
                for i in (0..n - 1).rev() {
                    node[i] = op(node[2 * i + 1], node[2 * i + 2])
                }
                SegIndexTree {
                    node: node,
                    zero: zero,
                    op: Box::new(op),
                    n: n,
                }
            }
            pub fn set(&mut self, mut x: i32, value: i64) {
                let y = x;
                x += self.n - 1;
                self.node[x] = (value, y);
                while x > 0 {
                    x = (x - 1) / 2;
                    self.node[x] = (self.op)(self.node[2 * x + 1], self.node[2 * x + 2]);
                }
            }
            pub fn get1(&self, i: i32) -> (i64, i32) {
                self.getrec(i..i + 1, 0, 0..self.n)
            }
            pub fn get<T>(&self, query: T) -> (i64, i32)
            where
                T: RangeBounds<i32>,
            {
                self.getrec(query.to_harfopen(0, self.n), 0, 0..self.n)
            }
            fn getrec(&self, query: Range<i32>, k: i32, range: Range<i32>) -> (i64, i32) {
                if query.separate_range(&range) {
                    return (self.zero, 0);
                }
                if query.contain_range(&range) {
                    return self.node[k];
                }
                let vl = self.getrec(
                    query.clone(),
                    2 * k + 1,
                    range.start..(range.start + range.end) / 2,
                );
                let vr = self.getrec(
                    query.clone(),
                    2 * k + 2,
                    (range.start + range.end) / 2..range.end,
                );
                (self.op)(vl, vr)
            }
        }
    }
}
pub mod modulo {
    use crate::independent::integer::Int;
    use std::marker::PhantomData;
    use std::ops::*;
    #[derive(Debug, PartialEq, Eq, Copy, Clone, Hash, PartialOrd, Ord)]
    pub struct ModInt<T>(pub i64, PhantomData<*const T>);
    impl<T: ConstValue> ModInt<T> {
        pub fn new<U: Int>(a: U) -> ModInt<T> {
            let x = a.to_i64();
            if x < 0 {
                ModInt::raw(x % T::M + T::M)
            } else if x < T::M {
                ModInt::raw(x)
            } else {
                ModInt::raw(x % T::M)
            }
        }
        pub fn pow<U: Int>(self, x: U) -> Self {
            let mut n = x.to_i64();
            let mut a = self;
            let mut res = Self::raw(1);
            while n > 0 {
                if n & 1 == 1 {
                    res *= a;
                }
                a = a * a;
                n >>= 1;
            }
            res
        }
        pub fn inv(self) -> Self {
            self.pow(T::M - 2)
        }
        #[inline]
        fn raw(x: i64) -> ModInt<T> {
            ModInt(x, PhantomData)
        }
    }
    pub trait ConstValue: PartialEq + Eq + Copy + Clone + std::hash::Hash + Ord {
        const M: i64;
    }
    impl<T> std::fmt::Display for ModInt<T> {
        fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
            write!(f, "{}", self.0)
        }
    }
    macro_rules ! impl_from_for_modint { ( $ ( $ tpe : ident ) ,* ) => { $ ( impl < T : ConstValue > From <$ tpe > for ModInt < T > { fn from ( n : $ tpe ) -> Self { Self :: new ( n ) } } ) * } ; }
    impl_from_for_modint!(u8, u16, u32, u64, u128, i8, i16, i32, i64, i128, usize, isize);
    impl<T: ConstValue> Add for ModInt<T> {
        type Output = ModInt<T>;
        fn add(self, other: ModInt<T>) -> ModInt<T> {
            let mut ret = self.0 + other.0;
            if ret >= T::M {
                ret -= T::M;
            }
            Self::raw(ret)
        }
    }
    impl<T: ConstValue> AddAssign for ModInt<T> {
        fn add_assign(&mut self, other: Self) {
            *self = self.add(other);
        }
    }
    impl<T: ConstValue> Sub for ModInt<T> {
        type Output = ModInt<T>;
        fn sub(self, other: ModInt<T>) -> ModInt<T> {
            let mut ret = self.0 + T::M - other.0;
            if ret >= T::M {
                ret -= T::M
            }
            Self::raw(ret)
        }
    }
    impl<T: ConstValue> SubAssign for ModInt<T> {
        fn sub_assign(&mut self, other: Self) {
            *self = self.sub(other);
        }
    }
    impl<T: ConstValue> Mul for ModInt<T> {
        type Output = ModInt<T>;
        fn mul(self, other: ModInt<T>) -> ModInt<T> {
            Self::raw(self.0 * other.0 % T::M)
        }
    }
    impl<T: ConstValue> MulAssign for ModInt<T> {
        fn mul_assign(&mut self, other: Self) {
            *self = self.mul(other);
        }
    }
    impl<T: ConstValue> Div for ModInt<T> {
        type Output = ModInt<T>;
        fn div(self, other: ModInt<T>) -> ModInt<T> {
            self * other.inv()
        }
    }
    impl<T: ConstValue> DivAssign for ModInt<T> {
        fn div_assign(&mut self, other: Self) {
            *self = self.div(other);
        }
    }
    impl<T: ConstValue> Rem for ModInt<T> {
        type Output = ModInt<T>;
        fn rem(self, other: ModInt<T>) -> ModInt<T> {
            Self::raw(self.0 % other.0)
        }
    }
    #[macro_export]
    macro_rules! modint {
        ( ) => {
            modint!(1000000007);
        };
        ( $ m : expr ) => {
            #[derive(Debug, PartialEq, Eq, Copy, Clone, Hash, PartialOrd, Ord)]
            pub enum __M {}
            impl $crate::modulo::ConstValue for __M {
                const M: i64 = $m;
            }
            #[allow(dead_code)]
            type Z = $crate::modulo::ModInt<__M>;
        };
    }
    macro_rules ! impl_integer_functions { ( $ ( $ tofn : ident , $ fromfn : ident , $ tpe : ident ) ,* ) => { $ ( fn $ tofn ( & self ) -> $ tpe { self . 0 as $ tpe } fn $ fromfn ( x : $ tpe ) -> Self { Self :: new ( x ) } ) * } ; }
    impl<T: ConstValue> Int for ModInt<T> {
        impl_integer_functions!(
            to_u8, from_u8, u8, to_u16, from_u16, u16, to_u32, from_u32, u32, to_u64, from_u64,
            u64, to_u128, from_u128, u128, to_i8, from_i8, i8, to_i16, from_i16, i16, to_i32,
            from_i32, i32, to_i64, from_i64, i64, to_i128, from_i128, i128, to_usize, from_usize,
            usize, to_isize, from_isize, isize
        );
        fn zero() -> Self {
            Self::new(0)
        }
        fn one() -> Self {
            Self::new(1)
        }
    }
}
pub mod ext {
    pub mod range {
        use crate::independent::integer::Int;
        use std::cmp::{max, min};
        use std::ops::{Bound, Range, RangeBounds, RangeInclusive};
        pub trait RangeEx<T> {
            fn width(&self) -> T;
            fn empty(&self) -> bool;
            fn contain_range(&self, inner: &Self) -> bool;
            fn separate_range(&self, other: &Self) -> bool;
            type ReturnRange;
            fn overlap(&self, other: &Self) -> Self::ReturnRange;
        }
        impl<T: Int> RangeEx<T> for Range<T> {
            fn width(&self) -> T {
                if self.empty() {
                    T::zero()
                } else {
                    self.end - self.start
                }
            }
            fn empty(&self) -> bool {
                !(self.start < self.end)
            }
            fn contain_range(&self, inner: &Self) -> bool {
                self.start <= inner.start && inner.end <= self.end
            }
            fn separate_range(&self, other: &Self) -> bool {
                self.end <= other.start || other.end <= self.start
            }
            type ReturnRange = Range<T>;
            fn overlap(&self, other: &Self) -> Self::ReturnRange {
                let left = max(self.start, other.start);
                let right = min(self.end, other.end);
                left..right
            }
        }
        impl<T: Int> RangeEx<T> for RangeInclusive<T> {
            fn width(&self) -> T {
                if self.empty() {
                    T::zero()
                } else {
                    *self.end() - *self.start() + T::one()
                }
            }
            fn empty(&self) -> bool {
                !(self.start() <= self.end())
            }
            fn contain_range(&self, inner: &Self) -> bool {
                self.start() <= inner.start() && inner.end() <= self.end()
            }
            fn separate_range(&self, other: &Self) -> bool {
                self.end() <= other.start() || other.end() <= self.start()
            }
            type ReturnRange = RangeInclusive<T>;
            fn overlap(&self, other: &Self) -> Self::ReturnRange {
                let left = *max(self.start(), other.start());
                let right = *min(self.end(), other.end());
                left..=right
            }
        }
        pub trait IntRangeBounds<U: Int>: RangeBounds<U> {
            #[doc = " inclusive"]
            fn lower_bound(&self, lower_bound: U) -> U {
                match self.start_bound() {
                    Bound::Included(x) => max(lower_bound, *x),
                    Bound::Excluded(x) => max(lower_bound, *x + U::one()),
                    Bound::Unbounded => lower_bound,
                }
            }
            #[doc = " exclusive"]
            fn upper_bound(&self, upper_bound: U) -> U {
                match self.end_bound() {
                    Bound::Included(x) => min(upper_bound, *x + U::one()),
                    Bound::Excluded(x) => min(upper_bound, *x),
                    Bound::Unbounded => upper_bound,
                }
            }
            fn to_harfopen(&self, lb: U, ub: U) -> Range<U> {
                self.lower_bound(lb)..self.upper_bound(ub)
            }
        }
        impl<T: ?Sized, U: Int> IntRangeBounds<U> for T where T: RangeBounds<U> {}
    }
}
pub mod macros {
    #[macro_export]
    macro_rules ! for_ { ( $ init : stmt ; $ cond : expr ; $ incr : expr , $ body : block ) => { $ init while $ cond { $ body $ incr ; } } ; }
    #[macro_export]
    macro_rules! chmax {
        ( $ x : expr , $ y : expr ) => {
            if $x < $y {
                $x = $y;
                true
            } else {
                false
            }
        };
    }
    #[macro_export]
    macro_rules! chmin {
        ( $ x : expr , $ y : expr ) => {
            if $x > $y {
                $x = $y;
                true
            } else {
                false
            }
        };
    }
    #[macro_export]
    macro_rules ! min { ( $ a : expr $ ( , ) * ) => { { $ a } } ; ( $ a : expr , $ b : expr $ ( , ) * ) => { { std :: cmp :: min ( $ a , $ b ) } } ; ( $ a : expr , $ ( $ rest : expr ) ,+ $ ( , ) * ) => { { std :: cmp :: min ( $ a , min ! ( $ ( $ rest ) ,+ ) ) } } ; }
    #[macro_export]
    macro_rules ! max { ( $ a : expr $ ( , ) * ) => { { $ a } } ; ( $ a : expr , $ b : expr $ ( , ) * ) => { { std :: cmp :: max ( $ a , $ b ) } } ; ( $ a : expr , $ ( $ rest : expr ) ,+ $ ( , ) * ) => { { std :: cmp :: max ( $ a , max ! ( $ ( $ rest ) ,+ ) ) } } ; }
    #[macro_export]
    macro_rules ! assign { ( $ arr : ident $ ( [ $ a : expr ] ) + = $ right : expr ) => { assign ! ( $ arr , $ ( [ $ a ] ) + , = , $ right , default ) ; } ; ( $ arr : ident $ ( [ $ a : expr ] ) + += $ right : expr ) => { assign ! ( $ arr , $ ( [ $ a ] ) + , += , $ right , default ) ; } ; ( $ arr : ident $ ( [ $ a : expr ] ) + -= $ right : expr ) => { assign ! ( $ arr , $ ( [ $ a ] ) + , -= , $ right , default ) ; } ; ( $ arr : ident $ ( [ $ a : expr ] ) + |= $ right : expr ) => { assign ! ( $ arr , $ ( [ $ a ] ) + , |= , $ right , default ) ; } ; ( $ arr : ident $ ( [ $ a : expr ] ) + &= $ right : expr ) => { assign ! ( $ arr , $ ( [ $ a ] ) + , &= , $ right , default ) ; } ; ( $ arr : ident $ ( [ $ a : expr ] ) + ^= $ right : expr ) => { assign ! ( $ arr , $ ( [ $ a ] ) + , ^= , $ right , default ) ; } ; ( $ arr : ident $ ( [ $ a : expr ] ) + min $ right : expr ) => { assign ! ( $ arr , $ ( [ $ a ] ) + , ^= , $ right , min ) ; } ; ( $ arr : ident $ ( [ $ a : expr ] ) + max $ right : expr ) => { assign ! ( $ arr , $ ( [ $ a ] ) + , ^= , $ right , max ) ; } ; ( $ arr : expr , [ $ head : expr ] , $ op : tt , $ right : expr , default ) => { let head = $ head ; if ( 0 ..$ arr . ilen ( ) ) . contains ( &$ head ) { let tmp = $ right ; $ arr [ head ] $ op tmp ; } } ; ( $ arr : expr , [ $ head : expr ] , $ op : tt , $ right : expr , min ) => { let head = $ head ; if ( 0 ..$ arr . ilen ( ) ) . contains ( &$ head ) { let tmp = $ right ; $ arr [ head ] = std :: cmp :: min ( $ arr [ head ] , tmp ) ; } } ; ( $ arr : expr , [ $ head : expr ] , $ op : tt , $ right : expr , max ) => { let head = $ head ; if ( 0 ..$ arr . ilen ( ) ) . contains ( &$ head ) { let tmp = $ right ; $ arr [ head ] = std :: cmp :: max ( $ arr [ head ] , tmp ) ; } } ; ( $ arr : expr , [ $ head : expr ] $ ( [ $ a : expr ] ) +, $ op : tt , $ right : expr , $ kind : ident ) => { let head = $ head ; if ( 0 ..$ arr . ilen ( ) ) . contains ( &$ head ) { assign ! ( $ arr [ head ] , $ ( [ $ a ] ) +, $ op , $ right , $ kind ) ; } } ; }
    #[macro_export]
    macro_rules! unwrap {
        ( $ arg : expr ) => {{
            let tmp = $arg;
            if tmp.is_none() {
                return;
            }
            tmp.unwrap()
        }};
    }
    #[macro_export]
    macro_rules! swap {
        ( $ a : expr , $ b : expr ) => {
            let tmp = $a;
            $a = $b;
            $b = tmp;
        };
    }
}
pub mod independent {
    pub mod integer {
        pub trait Int:
            std::ops::Add<Output = Self>
            + std::ops::Sub<Output = Self>
            + std::ops::Mul<Output = Self>
            + std::ops::Div<Output = Self>
            + std::ops::Rem<Output = Self>
            + std::ops::AddAssign
            + std::ops::SubAssign
            + std::ops::MulAssign
            + std::ops::DivAssign
            + std::hash::Hash
            + PartialEq
            + Eq
            + PartialOrd
            + Ord
            + Copy
        {
            fn to_u8(&self) -> u8;
            fn to_u16(&self) -> u16;
            fn to_u32(&self) -> u32;
            fn to_u64(&self) -> u64;
            fn to_u128(&self) -> u128;
            fn to_i8(&self) -> i8;
            fn to_i16(&self) -> i16;
            fn to_i32(&self) -> i32;
            fn to_i64(&self) -> i64;
            fn to_i128(&self) -> i128;
            fn to_usize(&self) -> usize;
            fn to_isize(&self) -> isize;
            fn from_u8(x: u8) -> Self;
            fn from_u16(x: u16) -> Self;
            fn from_u32(x: u32) -> Self;
            fn from_u64(x: u64) -> Self;
            fn from_u128(x: u128) -> Self;
            fn from_i8(x: i8) -> Self;
            fn from_i16(x: i16) -> Self;
            fn from_i32(x: i32) -> Self;
            fn from_i64(x: i64) -> Self;
            fn from_i128(x: i128) -> Self;
            fn from_usize(x: usize) -> Self;
            fn from_isize(x: isize) -> Self;
            fn zero() -> Self;
            fn one() -> Self;
            fn next(&self) -> Self {
                *self + Self::one()
            }
        }
        macro_rules ! impl_integer_functions { ( $ selftpe : ident , $ ( $ tofn : ident , $ fromfn : ident , $ tpe : ident ) ,* ) => { $ ( fn $ tofn ( & self ) -> $ tpe { * self as $ tpe } fn $ fromfn ( x : $ tpe ) -> Self { x as $ selftpe } ) * } ; }
        macro_rules ! impl_integer { ( $ ( $ tpe : ident ) ,* ) => { $ ( impl Int for $ tpe { impl_integer_functions ! ( $ tpe , to_u8 , from_u8 , u8 , to_u16 , from_u16 , u16 , to_u32 , from_u32 , u32 , to_u64 , from_u64 , u64 , to_u128 , from_u128 , u128 , to_i8 , from_i8 , i8 , to_i16 , from_i16 , i16 , to_i32 , from_i32 , i32 , to_i64 , from_i64 , i64 , to_i128 , from_i128 , i128 , to_usize , from_usize , usize , to_isize , from_isize , isize ) ; fn zero ( ) -> Self { 0 } fn one ( ) -> Self { 1 } } ) * } ; }
        impl_integer!(u8, u16, u32, u64, u128, i8, i16, i32, i64, i128, usize, isize);
    }
}
pub mod query {
    pub mod imosm {
        use crate::arraylist::List;
        use crate::{ext::range::IntRangeBounds, independent::integer::Int};
        use std::ops::RangeBounds;
        pub fn imos<T: RangeBounds<i32>, I: Int>(n: i32, ranges: &List<(T, I)>) -> List<I> {
            let mut ret = List::init(I::zero(), n);
            for (r, d) in ranges.iter().map(|r| (r.0.to_harfopen(0, n), r.1)) {
                ret[r.start] += d;
                if r.end < n {
                    ret[r.end] -= d;
                }
            }
            for i in 0..n {
                if i > 0 {
                    ret[i] = ret[i] + ret[i - 1];
                }
            }
            ret
        }
    }
}
pub mod scanner {
    use crate::arraylist::List;
    use std::io::{stdin, BufReader, Bytes, Read, Stdin};
    use std::str::FromStr;
    pub struct Scanner {
        buf: Bytes<BufReader<Stdin>>,
    }
    impl Scanner {
        pub fn new() -> Scanner {
            Scanner {
                buf: BufReader::new(stdin()).bytes(),
            }
        }
        pub fn read_next<T: FromStr>(&mut self) -> Option<T> {
            let token = self
                .buf
                .by_ref()
                .map(|c| c.unwrap() as char)
                .skip_while(|c| c.is_whitespace())
                .take_while(|c| !c.is_whitespace())
                .collect::<String>();
            token.parse::<T>().ok()
        }
        pub fn read<T: FromStr>(&mut self) -> T {
            self.read_next().unwrap()
        }
        pub fn readn<T: FromStr>(&mut self, n: i32) -> List<T> {
            (0..n).map(|_| self.read::<T>()).collect()
        }
        pub fn chars(&mut self) -> List<char> {
            self.read::<String>().chars().collect()
        }
    }
}
pub mod arraylist {
    use crate::{ext::range::IntRangeBounds, independent::integer::Int};
    use std::fmt::Formatter;
    use std::iter::FromIterator;
    use std::ops::{Index, IndexMut, RangeBounds};
    use std::slice::Iter;
    #[derive(Clone, PartialEq, Eq)]
    pub struct List<T> {
        pub vec: Vec<T>,
    }
    impl<T> List<T> {
        #[inline]
        pub fn new() -> List<T> {
            List { vec: vec![] }
        }
        #[inline]
        pub fn init(init: T, n: i32) -> List<T>
        where
            T: Clone,
        {
            List {
                vec: vec![init; n as usize],
            }
        }
        #[inline]
        pub fn from_vec(vec: Vec<T>) -> List<T> {
            List { vec }
        }
        #[inline]
        pub fn ilen(&self) -> i32 {
            self.vec.len() as i32
        }
        #[inline]
        pub fn iter(&self) -> Iter<'_, T> {
            self.vec.iter()
        }
        #[inline]
        pub fn push(&mut self, item: T) {
            self.vec.push(item);
        }
        #[inline]
        pub fn sort(&mut self)
        where
            T: Ord,
        {
            self.vec.sort();
        }
        #[inline]
        pub fn reverse(&mut self) {
            self.vec.reverse();
        }
        #[inline]
        pub fn sort_by<F>(&mut self, compare: F)
        where
            F: FnMut(&T, &T) -> std::cmp::Ordering,
        {
            self.vec.sort_by(compare)
        }
        #[inline]
        pub fn sort_by_key<K, F>(&mut self, compare: F)
        where
            F: FnMut(&T) -> K,
            K: Ord,
        {
            self.vec.sort_by_key(compare)
        }
        #[inline]
        pub fn first(&self) -> Option<&T> {
            self.vec.first()
        }
        #[inline]
        pub fn last(&self) -> Option<&T> {
            self.vec.last()
        }
        #[inline]
        pub fn pop(&mut self) -> Option<T> {
            self.vec.pop()
        }
        #[inline]
        pub fn swap(&mut self, i: i32, j: i32) {
            self.vec.swap(i as usize, j as usize);
        }
        #[inline]
        pub fn append(&mut self, mut other: Self) {
            self.vec.append(&mut other.vec);
        }
        #[inline]
        pub fn extend(&mut self, other: impl Iterator<Item = T>) {
            self.vec.extend(other);
        }
        #[inline]
        pub fn mirror(&self) -> std::iter::Cloned<Iter<T>>
        where
            T: Clone,
        {
            self.iter().cloned()
        }
        #[inline]
        pub fn map<B, F>(&self, f: F) -> List<B>
        where
            T: Clone,
            F: FnMut(T) -> B,
        {
            self.mirror().map(f).collect()
        }
        #[inline]
        pub fn filter<P>(&self, predicate: P) -> List<T>
        where
            T: Clone,
            P: FnMut(&T) -> bool,
        {
            self.mirror().filter(predicate).collect()
        }
        #[inline]
        pub fn filter_map<B, F>(&self, f: F) -> List<B>
        where
            T: Clone,
            F: FnMut(T) -> Option<B>,
        {
            self.mirror().filter_map(f).collect()
        }
        #[inline]
        pub fn any<P>(&self, predicate: P) -> bool
        where
            P: FnMut(&T) -> bool,
        {
            self.iter().any(predicate)
        }
        #[inline]
        pub fn all<P>(&self, predicate: P) -> bool
        where
            P: FnMut(&T) -> bool,
        {
            self.iter().all(predicate)
        }
        #[inline]
        pub fn sum(&self) -> T
        where
            T: Int,
        {
            self.iter().cloned().fold(T::zero(), |acc, x| acc + x)
        }
        #[inline]
        pub fn enumerate(&self) -> List<(i32, T)>
        where
            T: Clone,
        {
            self.mirror()
                .enumerate()
                .map(|p| (p.0 as i32, p.1))
                .collect()
        }
        #[inline]
        pub fn find<P>(&self, mut predicate: P) -> Option<&T>
        where
            P: FnMut(&T) -> bool,
        {
            self.iter().find(|x| predicate(*x))
        }
        #[inline]
        pub fn index_of<P>(&self, mut predicate: P) -> Option<i32>
        where
            P: FnMut(&T) -> bool,
        {
            self.iter()
                .enumerate()
                .find(|&(_i, x)| predicate(x))
                .map(|p| p.0 as i32)
        }
        #[inline]
        pub fn to<B: FromIterator<T>>(&self) -> B
        where
            T: Clone,
        {
            self.mirror().collect()
        }
        #[inline]
        pub fn min(&self) -> Option<&T>
        where
            T: Ord,
        {
            self.iter().min()
        }
        #[inline]
        pub fn max(&self) -> Option<&T>
        where
            T: Ord,
        {
            self.iter().max()
        }
        #[inline]
        pub fn argmin(&self) -> Option<i32>
        where
            T: Ord,
        {
            let item = self.iter().min()?;
            self.iter()
                .enumerate()
                .find(|p| p.1 == item)
                .map(|p| p.0 as i32)
        }
        #[inline]
        pub fn argmax(&self) -> Option<i32>
        where
            T: Ord,
        {
            let item = self.iter().max()?;
            self.iter()
                .enumerate()
                .find(|p| p.1 == item)
                .map(|p| p.0 as i32)
        }
        #[inline]
        pub fn part<U>(&self, range: U) -> List<T>
        where
            T: Clone,
            U: RangeBounds<i32>,
        {
            List::from_vec(
                self.vec[range.lower_bound(0) as usize..range.upper_bound(self.ilen()) as usize]
                    .to_vec(),
            )
        }
        #[inline]
        pub fn first_exn(&self) -> &T {
            self.first().unwrap()
        }
        #[inline]
        pub fn last_exn(&self) -> &T {
            self.last().unwrap()
        }
        #[inline]
        pub fn pop_exn(&mut self) -> T {
            self.pop().unwrap()
        }
        #[inline]
        pub fn min_exn(&self) -> &T
        where
            T: Ord,
        {
            self.min().unwrap()
        }
        #[inline]
        pub fn max_exn(&self) -> &T
        where
            T: Ord,
        {
            self.max().unwrap()
        }
        #[inline]
        pub fn argmin_exn(&self) -> i32
        where
            T: Ord,
        {
            self.argmin().unwrap()
        }
        #[inline]
        pub fn argmax_exn(&self) -> i32
        where
            T: Ord,
        {
            self.argmax().unwrap()
        }
        #[inline]
        pub fn find_exn<P>(&self, predicate: P) -> &T
        where
            P: FnMut(&T) -> bool,
        {
            self.find(predicate).unwrap()
        }
        #[inline]
        pub fn index_of_exn<P>(&self, predicate: P) -> i32
        where
            P: FnMut(&T) -> bool,
        {
            self.index_of(predicate).unwrap()
        }
    }
    impl<T> Index<i32> for List<T> {
        type Output = T;
        #[inline]
        fn index(&self, index: i32) -> &Self::Output {
            if cfg!(debug_assertions) {
                self.vec.index(index as usize)
            } else {
                unsafe { self.vec.get_unchecked(index as usize) }
            }
        }
    }
    impl<T> IndexMut<i32> for List<T> {
        #[inline]
        fn index_mut(&mut self, index: i32) -> &mut Self::Output {
            if cfg!(debug_assertions) {
                self.vec.index_mut(index as usize)
            } else {
                unsafe { self.vec.get_unchecked_mut(index as usize) }
            }
        }
    }
    impl<T> FromIterator<T> for List<T> {
        fn from_iter<U: IntoIterator<Item = T>>(iter: U) -> Self {
            let mut vec = vec![];
            for i in iter {
                vec.push(i);
            }
            List { vec }
        }
    }
    impl<T> IntoIterator for List<T> {
        type Item = T;
        type IntoIter = std::vec::IntoIter<T>;
        fn into_iter(self) -> std::vec::IntoIter<T> {
            self.vec.into_iter()
        }
    }
    impl<'a, T> IntoIterator for &'a List<T> {
        type Item = &'a T;
        type IntoIter = Iter<'a, T>;
        fn into_iter(self) -> Iter<'a, T> {
            self.vec.iter()
        }
    }
    impl<T: std::fmt::Display> std::fmt::Display for List<T> {
        fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
            write!(
                f,
                "{}",
                self.iter()
                    .map(|x| format!("{}", x))
                    .collect::<Vec<_>>()
                    .join(" ")
            )
        }
    }
    impl<T: std::fmt::Debug> std::fmt::Debug for List<T> {
        fn fmt(&self, f: &mut Formatter<'_>) -> std::fmt::Result {
            write!(
                f,
                "[{}]",
                self.iter()
                    .map(|x| format!("{:?}", x))
                    .collect::<Vec<_>>()
                    .join(", ")
            )
        }
    }
    impl<T> From<Vec<T>> for List<T> {
        fn from(vec: Vec<T>) -> Self {
            Self::from_vec(vec)
        }
    }
    impl<T: Clone> From<&[T]> for List<T> {
        fn from(slice: &[T]) -> Self {
            slice.iter().cloned().collect()
        }
    }
    #[macro_export]
    macro_rules ! list { ( ) => { $ crate :: arraylist :: List :: new ( ) } ; ( $ v : expr ; $ a : expr ) => { $ crate :: arraylist :: List :: init ( $ v , $ a ) } ; ( $ v : expr ; $ a : expr ; $ ( $ rest : expr ) ;+ ) => { $ crate :: arraylist :: List :: init ( list ! ( $ v ; $ ( $ rest ) ;+ ) , $ a ) } ; }
}